Modeling On-Body DTN Packet Routing Delay in the Presence of Postural Disconnections

1.1. Body Area Networks

A number of tiny wireless sensors, strategically placed or implanted on a patient's body, can create a Wireless Body Area Network (WBAN) [1, 2]. A WBAN can monitor vital signs, providing real-time feedback for enabling many patient diagnostics procedures via continuous monitoring of chronic conditions, or recovery progress from an illness or surgical procedure. Data transaction across such sensors can be point-to-point or multipoint-to-point. While distributed detection of an athlete's posture [3, 4] would require point-to-point packet exchange across various on-body sensors, applications such as monitoring vital signs, as shown in Figure 1, will require all body-mounted and/or implanted sensors [2, 5] to route data multipoint-to-point to a sink node, which in turn can process and relay the information wirelessly to an out-of-body server. Data transaction can be also real-time or nonreal-time. While patient monitoring type of applications would require real-time packet routing, monitoring an athlete's physiological data can be collected offline for postprocessing and analysis purposes. The routing protocols modeled in this paper cater to this nonreal-time class of on-body applications.

1.2. Short RF Range

1.3. Routing with Network Partitioning

Low RF ranges also mean that postural body movements can give rise to frequent partitioning or disconnection in WBAN topologies, resulting in a body area Delay Tolerant Network (DTN) [12–17]. Such topological partitioning can often get aggravated by the unpredictable RF attenuation caused due to signal blockage by clothing material and body segments. Although real-time applications such as patient monitoring may not be supported in the presence of topological partitioning, nonreal-time applications such as athlete's physiology monitoring can still be supported using on-body DTN packet routing across disconnected partitions. Performance goals for such protocols will be to obtain ( ) low end-to-end delay, ( ) low packet loss, and ( ) low transmission energy consumption.

1.4. Novelty and Contributions

The goal of this paper is to develop analytical modeling mechanisms for computing packet transfer delay for a series of DTN routing algorithms that can be implemented in an on-body setting. Although a number of papers in the literature [12–17] have studied DTN routing in general settings, to our knowledge, this is the first study that formally evaluates DTN routing delay in a WBAN through analytical model development. The dominating delay in DTN routing is contributed by packet buffering caused due to topological disconnections. In the absence of network congestions in low data-rate WBANs, such buffering delays are usually much larger compared to the congestion delay. That is why the congestion delay is not modeled in this paper. Specific contributions of the paper are as follows. First, we develop a prototype body area network for motivating the on-body packet routing problem and conducting on-body routing experiments with the DTN routing protocols that are modeled and evaluated in this paper. Second, a topology trace collection mechanism is developed for wirelessly extracting network topology, as a function of human postural dynamics, from the on-body sensors to an off-body server. Third, analytical techniques are developed for modeling the end-to-end packet delay for a range of DTN routing algorithms, namely, opportunistic [18–20] utility based [18, 20, 21], random [18, 20, 22], PRMPL [23, 24], and DVRPLC [23, 24]. Fourth, the DTN routing delays obtained from the developed model are compared with results from on-body experiments from the prototype WBAN and off-body simulation carried out on network topology traces obtained from the prototype WBAN. Finally, using the model and the topology trace data, a detailed analysis is carried out for identifying noncritical nodes in order to design a minimal WBAN topology from the routing stand point. The novelty of this approach includes ( ) experimental evaluation of the proposed framework in a practical prototype WBAN system and ( ) development of detailed delay models that can be useful for predeployment system dimensioning, planning, and what-if analysis of real body area networks.

3.1. WBAN Prototype

A Wireless Body Area Network (WBAN) is constructed by mounting seven sensor nodes (attached on two upper-arms, two thighs, two ankles, and one in the waist area) as shown in Figure 1. Each wearable node consists of a 900 MHz Mica2Dot MOTE (running TinyOS operating system), with Chipcon's SmartRF CC1000 radio chip (http://www.chipcon.com/), and the sensor card MTS510 from Crossbow Inc. (http://www.xbow.com/). The Mica2Dot nodes run from a 570 mAH button cell with a total sensor weight of approximately 10 grams. The default CSMA MAC protocol is used with a data rate of 19.2 kbps.

Via software adjustments of the CC1000's transmission power, the transmission range is set to be in between 0.3 m–0.6 m. By doing so, we are able to emulate the ultralow transmission range for the embedded transceivers [8–11] as reported in the literature. Note that the variation of the range is caused due to the variability in antenna orientation, clothing, and other on-body RF attenuation characteristics.

The sensors form a mesh topology with one or multiple simultaneous network partitions. The topology and the number of partitions change dynamically based on the postural positions of the subject individuals. All experiments in this paper correspond to multipoint-to-point routing in which data from all other nodes are sent to node-6 (see Figure 1), which is designated as the on-body sink node. This node collects raw data and sends processed results or events to an out-of-body server using a wireless link. This external link is created between the on-body sink node and to an out-of-body Mica2Dot radio node connected to a Windows PC through a custom-built serial interface, running RS232 protocol.

3.2. Variations of Topology and Network Partitions

Experiments were carried out for observing the impacts of postural mobility on network partitioning. A human subject, fitted with seven sensors, was asked to follow a predetermined sequence of postures (SIT, SIT-RECLINING, LYING-DOWN, STAND, WALK, and RUN), each lasting for 20 sec. The status of three WBAN links (1–3, 4–6, and 5–3) during such an experiment is shown in Figure 2. The presence and absence of a link's connectivity, as sampled by the nodes on the link, is represented by 1 and 0, respectively.

Each node maintains a neighbor table based on Hello messages sent periodically with low transmission power once in 1.4 sec. A time-out period of 2.8 sec. is used for purging entries from the neighbor table. The link status in Figure 2 is constructed by combining the neighbor table information from the nodes relevant for the exhibited links. Experimentally, the neighbor table information is periodically sent by all seven on-body nodes to the out-of-body server (in Figure 1) using the full transmission power of the Chipcon's CC1000 radio.

The following observations can be made from Figure 2. First, few links are connected only during certain postures, which can lead to significant topology variations and network partitioning across the postures. For instance, link 5–3 (between left front thigh and upper left arm nodes) shows the effect of distance on connectivity. The link is connected during most closed postures such as SIT and REC. However, for the stretched out postures such as LYING-DOWN, STAND, and WALK, the link is mostly disconnected. Similar trends are observed for the other links including link 1–3 and link 4–6, as shown in Figure 2.

The second observation is that even within a posture, a link may have intermittent disconnections (e.g., link 1–3 is disconnected during the SIT posture from "0–20" sec. interval). The reasons for such intraposture disconnections include minor body movements, RF signal blockage by body segments and clothing material, and also the relative orientations of the node-pairs forming the link in question.

The topology level impacts of the body posture variation are reported in Figure 3. Observe the wide swing of the node degree (1.5 to 3.8 across the six postures/activities) which indicates a high level of dynamism in the on-body mesh topology. Also observe the number of simultaneous network partitions which vary from 1 to 5, indicating frequent topological partitioning as hypothesized in Section 1.3. As expected, the postures with relatively lower node degree correspond to higher number of network partitions. Such topological disconnections necessitate on-body store-and-forward routing.

5.1. Opportunistic Routing

In DTN opportunistic routing (OPPT) [18–20] a source node delivers packet to the destination node only when the two nodes come into direct contact. This single copy mechanism offers a simple DTN routing approach in which the delay can be very large, especially in scenarios with low mobility or infrequent link formation between the source and destination. This protocol is simple to implement and suited well for the processing- and energy-constrained on-body sensors for which complex algorithms should be avoided. It is highly energy efficient due to the single transmission requirement for each packet delivery. However, the expected packet delivery delay for OPPT can be quite high, especially when the source and the destination nodes are rarely in direct contact with each other. The protocol is also very sensitive to the source-destination link quality since it relies only on that single direct link for all packet delivery. Opportunistic routing is modeled and analyzed in this section for estimating the worst case delay performance and for finding an upper-bound for packet delivery delay in a WBAN setting.

Since a source node delivers a packet to destination only when and a packet at node can be generated at any arbitrary time slot, the delivery delay for a packet is as developed in (2). This is true only when the packet generation rate is low enough so that no more than one packet is generated during a period (see Figure 5). This means that the generated packet can be delivered at the very beginning of the immediately following period without any additional wait.

However, when the packet generation rate is higher so that multiple packets are generated during a period, the packets need to be delivered one per time slot during the next period. This backlog clearance adds an additional delay component that needs to be added in addition to the from (2). Let represent the number of packets generated during the period. With being the packet generation rate at the source node , . After the subsequent period starts, these packets are flushed one packet per time slot, requiring time slots. During these slots, another packets are generated which are then cleared one per slot.

Combining the backlog clearance delay with the Expected Link Delay (ELD), the average delivery delay for the packets generated during the period can be written as . Average delay for the packets generated during the period can be written as . Therefore, the overall average packet delay for on-body opportunistic routing can be expressed as

(3)

or

(4)

where Expected Link Delay (ELD) can be computed in (2) and . Note that this expression is valid when the system is stable in the sense that on an average, all packets generated during the and periods are able to be delivered during the period for the link between nodes and .

5.2. Randomized Routing

In randomized routing protocol (RAND), if a node with a data packet does not have a direct connection with the destination, the node forwards the data packet to a neighbor chosen at random [19, 20]. The packet is subsequently forwarded in the same way, till it is received at the destination. Unlike for hot-potato routing [20] in large networks, the delay performance of RAND can often be better than that of opportunistic routing in small body area networks only with few nodes. Smaller topologies have lesser number of end-to-end path combinations, leading to quicker delivery. Also, the network partitioning, as shown in Figure 3, helps reducing the path combinations even further. Packet looping, which is inherent in a randomized routing protocol, can be avoided by recording a packet's traversed path in it incrementally so that a forwarding filtering can be implemented. A packet is never forwarded to a node that is recorded in that packet's already traversed path. Like OPPT, the randomized protocol is also simple to implement but can deliver lower packet delay compared to OPPT. A packet being forwarded using the RAND protocol, however, can suffer from a large number of unnecessary forwarding before it is delivered at the destination. In other words, this protocol can be quite energy-inefficient.

Definition 3 (forwarding probability).

In RAND forwarding, a node- forwards a packet uniformly randomly to one of its currently connected neighbors. Therefore, at any time slot , the probability of node forwarding a packet to node is defined as

(5)

where is the number of nodes in the on-body network. Equation (5) is applicable as long as node currently has at least one neighbor , and none of those neighbors is the destination node (i.e., ). In case when node has destination as a current neighbor, the packet is forwarded to node with probability "1". Also, when node has no current neighbors, it keeps buffering the packet (i.e., ), resulting in for all . Incorporating all these situations, (5) can be expanded as

(6)

Definition 4 (forwarding matrix).

The forwarding matrix captures the forwarding probabilities at time slot across all possible links in the network with nodes and can be represented as

(7)

The Forwarding Matrix has two notable properties. First, the elements in the th row are all zeros since the destination node never forwards a packet. The elements in the th column, however, are either 1 or zero (not explicitly shown above), depending on node 's instantaneous connectivity with the other nodes as expressed above in (6). Second, the summation of all elements in all rows (except the th row) should be 1. The Forwarding Matrix, which depends on the link states , can be created after the forwarding probabilities are computed using (6) based on the observed link states from the collected WBAN topology traces.

Consider a data packet that is generated at node during the th time slot, and delivered to node at the th time slot, resulting in a delay of slots. The value of can vary from 0 to infinity. Let the probability of the above event (i.e., delivering the packet with a delay of slots) be represented as the delivery probability , which can be expressed as

(8)

which is the element of the product matrix for a packet generated at time slot and delivered at time . Equation (8) shows the probability of delivering a packet with a delay of slots, where can range from 0 to infinity. Therefore, the expected RAND forwarding delay for a packet that was generated at the th time slot can be written as

(9)

where is the length (in number of slots) of the experimental topology traces obtained in Section 4. Considering sufficiently long on-body topology traces (i.e., large ), the maximum value of in (9) is set to be instead of infinity.

To clarify the above forwarding concept further, let us explore the following example in Figure 6. Consider a 4-node (i.e., ) body sensor network with node-1 as the source and node-3 as the destination. Example forwarding matrixes , , and and the corresponding network topologies at time slots 1, 2, and 3, obtained from the topology trace, are given in Figure 6.

Using the above matrixes, the delay probabilities can be computed as , , and using (8). According to , at time slot 1, node-1 has two neighbors (2 and 4), node-2 has one neighbor (node-1), and node-4 has a direct connection with the destination node-3. Assume that a packet is generated at source (node-1) at time slot 1. Since node-1 has no direct connection with (i.e., ), the packet will be randomly forwarded to either node 2 or 4 with probability 0.5 each, but the probability of delivering it to the destination node-3 is zero in the current slot-1 (out of all possible infinite number of slots in future). This is captured by which is the [1, 3] element of matrix .

At time slot 2, the packet will be forwarded to 3 through 2 with probability 1, that is, if 2 has already received the packet in slot 1. Otherwise (i.e., the packet was forwarded to node 4 in slot 1), the packet will be forwarded to node-1 or node-2 by node-4 at slot 2. Therefore, the probability of delivering the packet to the destination node-3 in slot-2 (out of all possible slots) is 0.5. This is captured by from the [1, 3] element of the product matrix .

Since in , the packet is guaranteed to be delivered to node-3 in slot-3. Since the probability of delivery in slot-1 was zero, and in slot-2 was 0.5, and the delivery is guaranteed in slot-3 (i.e., if it was not delivered in slot-2), the probability of delivering the packet in slot-3 (out of all possible slots) is 0.5. In other words, the probability of delivery with a delay of 2 slots (i.e., ) is 0.5. This is also captured as from the [1, 3] element of the product matrix . Using , , and , the expected delay for random forwarding for this example WBAN topology trace is time slots.

5.3. Utility-Based Routing Using Link Locality

In randomized routing, a node does not consider the locality of its connectivity with other network nodes while forwarding a packet. In utility-based routing protocols [17–21], nodes prefer to forward packets to destination through the neighbor with the latest encounter with the destination, thus leveraging the link locality in the form of its age. Each node is assigned a utility value based on the last encounter time with the destination, and a packet is forwarded to a neighbor with the highest utility value. Utility represents how useful (fast) this node might be in delivering a data packet to the destination and is often implemented using a timer. The delay of utility-based routing is expected to be lower than that in OPPT and RAND routing. Also, the number of packet forwarding in utility-based routing is expected to be smaller compared to RAND, mainly because of its exploitation of the link connection locality while selecting the next-hop during packet forwarding. The implementation of this protocol, however, can be more complex than OPPT and RAND because each node needs to compute and maintain the utility information for all neighbors in the network. Therefore, for large networks, maintaining utility information for every node can create significant scalability concerns. However, for small WBAN s this is less of an issue because of their small node-counts.

Let the utility function represent the utility value, of node with respect to node at the th time slot. Every time node comes in contact with node , the quantity is set to a maximum utility value and then for every time slot the node remains out of contact from the destination, the quantity is decreased based on a preset utility reduction method [19, 21] as a function of elapsed time. The update rule for can be written as

(10)

where is the maximum possible utility value to the destination. These utility values are exchanged between neighbors within the periodic Hello messages.

With the above definition of utility, at the th time slot node- will forward a packet (destined to node- ) to node- only if and forall , where is the set of all neighbors of node- during the th time slot.

Note that the above forwarding logic assumes that each on-body node is guaranteed to intermittently come within up to 2-hop contact from the destination node. In other words, a source node is able to meet other nodes that intermittently come in direct contact with the destination node. In our experimental topology this assumption was always found true [24]. In fact for a WBAN topology, it is generally true that depending on the specific postural patterns, all nodes intermittently form direct links with all other nodes in the network. This observation makes the assumption generally applicable for WBANs which usually have a small network diameter [19, 21]. When this 2-hop reachability assumption is not valid in large WBANS, transitive components will need to be incorporated while computing the utility factor.

The packet routing delay in utility-based forwarding (UTILITY) can be computed using the same logic as in random forwarding (RAND) except that the forwarding probabilities in (6) need to be reformulated for UTILITY. The forwarding probability in this case can be expressed as

(11)

where represents the set of all on-body nodes and where is the set of all neighbors of node- during the th time slot. The top line of (11) represents a situation in which either node- does not have any neighbor during the th time slot, or its own utility to the destination node- is higher than those of all its current neighbors. Either way, the node buffers the packet with probability 1. The middle part of the equation codes the utility-based forwarding rule as stated after (11). The bottom part represents the situation in which the destination node- is a direct neighbor of node- , causing a direct delivery.

Once the forwarding probabilities are computed applying (11) on the on-body topology traces collected in Section 4, the forwarding matrix and the delivery probabilities are computed using the same rules presented in (7) and (8). Finally, the delivery delay is computed as using (9).

5.4. Probabilistic Routing with MultiScale Postural Locality (PRMPL)

Routing using PRMPL utilizes a Postural Link Cost(PLC) [23] which captures WBAN link localities in multiple time scales. For on-body packet forwarding, the PLC is used exactly the same way as for the UTILITY routing, that is, by replacing the utility values by the PLCs. With posture and activity changes of a human subject, the PLC link costs are automatically adjusted such that the packets are forwarded to next-hops which are most likely to provide an end-to-end path with minimum intermediate buffering/storage delays. PLC is defined as , , which represents the probability of finding . The update equations for PLC are formulated as [23, 24, 36]

(12)

According to (12), when the link is connected, thePostural Link Cost(PLC) increases at a rate determined by the constant , and the difference between the current value of and its maximum value, which is 1. As a result, if the link remains connected for a long time, the quantity asymptotically reaches its maximum value of 1. When the link is disconnected, asymptotically reaches zero with a rate determined by the constant . To summarize, for a given , responds to the instantaneous connectivity condition of the link .

With time invariant , the PLC update rules in (12) capture the locality in short-term link connectivity in a manner conceptually similar to the age-based utility formulation, as developed in [19, 21]. It is, however, not the same because in the designs in [19, 21], the routing utility of a link is increased incrementally when the link is formed and is reduced to zero as soon as the link is disconnected. This formulation of utility misses out the fact that even after disconnection, the formation probability of that link may be higher than a currently connected link. In other words, those definitions of utility fairly differentiate across currently connected links, but not across the currently nonconnected links. In the formulation of PLC in (12), motivated by the logic used in PROPHET [17], we track the short-term locality even when a link is not physically connected. This extended persistency in PLC is expected to improve performance over the existing age-based utility definitions as used in [19, 21].

The next design step is to dimension the parameter for capturing link localities at a longer time scale. From (12), the rate of change of the PLC per time slot can be written as

(13)

Equation (13) indicates that for a high (e.g., 0.9), increases fast when the link is connected and decreases slowly when the link is not connected. Conversely, for a low (e.g., 0.1), increases slowly when the link is connected and decreases fast when the link is not connected. Ideally, it is desirable that for a historically good link (i.e., connected frequently on a longer time scale), should increase fast and decrease slowly, and for a historically bad link, it should increase slowly and decrease fast. This implies that the parameter needs to capture the long-term history of the link; hence it should be link specific and time varying. Based on this observation, we define Historical Connectivity Quality (HCQ) of an on-body link at time slot as

(14)

The constant represents a measurement window (in number of slots) over which the connectivity quality is averaged. The factor , indicates the historical link quality as a fraction of time the link was connected during the last slots. The parameter should be chosen based on the human postural mobility time constants. Experimentally, we found the optimal values that work well for a large number of subject individuals and range of postures to be in between 7 sec. and 14 sec.

Figure 7 shows the evolution of PLC and HCQ with time. The top graph shows an example link activity (indicated by ) with the first half indicating a steadily connected link with a single time slot (1.4 sec.) of disconnection at time slot 10, and the second half indicates a steadily disconnected link with single slot of connection at the 41st slot. The top graph also shows the evolution of according to (14) with a set to 7 time slots. The bottom graph shows the evolution of with constant (i.e., 0.9 and 0.1) and link-specific time varying from (14), indicating the historical link quality. When the link is steadily well connected (during the first half), a high constant (i.e., 0.9) responds well to a momentary disconnection by decreasing slowly, but recovering quickly when the link becomes reconnected. A low constant (i.e., 0.1) responds poorly in this situation by doing just the opposite, that is, a fast decrease and slow recovery.

Similarly, when the link is steadily disconnected (during the second half), a low constant (i.e., 0.1) responds relatively better than a high constant (i.e., 0.9) by increasing slowly for a momentary connection, and decreasing quickly after the link becomes disconnected. The lines for two constant values clearly show that a single constant value for is not able to handle both good-link and bad-link situations equally effectively.

As hypothesized, the link-specific and time-varying , on the other hand, is able to handle both situations well by mimicking the behavior of during the historically good-link situation and that of during the historically bad-link situation. These results clearly demonstrate the effectiveness of the HCQ and PLC concepts for designing routing utilities that can capture both short and long-term localities of the on-body link dynamics. With this multi-scale approach, the proposed mechanism should be able to outperform both age-based (UTILITY) [19, 21] and probabilistic [17] routing protocols that use only short-term locality information.

Note that unlike the entities in Figures 2 and 3, the PLC and HCQ in Figure 7 show the link connectivity localities which depends on the short- and long-term history of the link. The localities captures in (12) and (14) are responsible for this memory-based behavior in Figure 7 in contrast to the instantaneous link behavior in Figures 2 and 3. Figure 8 summarizes the structural difference between PRMPL [36] and the UTILITY [19, 21] age-based protocol from the link locality capture standpoint. As shown in the figure, while UTILITY extracts only short-term locality from the link on-off dynamics, PRMPL extracts an additional long-term locality by observing the Historical Connectivity Quality (HCQ) as presented in (14). Additional complexity for PRMPL over OPPT, UTILITY, and RAND is expected due to its periodic computation of per-link HCQ and PLC.

The forwarding rule in PRMPL is identical to what stated for UTILITY-based forwarding in Section 5.3 with the utility function replaced by the postural link cost . Consequently, the forwarding probabilities , the forwarding matrix , and the delivery probabilities can be computed using (7), (8), and (11), respectively, and finally, the end-to-end packet delay can be computed as using (9).

5.5. Distance Vector Routing with Postural Link Costs (DVRPLC)

In DVRPLC, nodes maintain end-to-end cumulative path cost estimates to a common sink node. Let us define a Link Cost Factor (LCF) which represents the routing cost for the link (between nodes and ) during the discrete time slot . The update equations for LCF are formulated as [23, 24, 36]

(15)

When the link is connected, decreases at a rate determined by , where , is the Historical Connectivity Quality, as defined in (14). If the link remains connected for a long time, the quantity asymptotically reaches its minimum value 0. When the link remains disconnected, increases at a rate determined by the quantity and the difference between the current cost and its maximum value 1. This formulation ensures that a link's routing cost always reflects the likelihood of the existence of the link while capturing its historical connectivity trends. Note that the time evolution of LCF in DVRPLC follows a rationale that is very similar to that of PLC in PRMPL. The main difference is that while the LCF reduces for connected links, the PLC increases in such situations. Similar difference exists when a link remains disconnected. To summarize, like in PRMPL, the cost in DVRPC captures both short- and long-term link localities for minimum delay packet routing.

Let be the minimum end-to-end cumulative cost from node- to the sink node- . According to distance vector routing logic, when a node needs to forward a packet to the sink node and it meets a node , the packet is forwarded to node only if the condition is found true. In other words, a lower path cost through node indicates that the latter is more likely to forward the packet to node than what node 's chances are. That justifies the packet transfer from node to with a goal of minimizing the end-to-end packet routing delay.

Note that the DVRPLC protocol attempts to minimize end-to-end cumulative routing costs. The objective is that due to this end-to-end cost minimization, DVRPLC should be able to outperform (from a delay standpoint) PRMPL which always interprets its PLC only at the link level and not in an end-to-end cumulative manner.

To execute DVRPLC, each on-body sensor node- uses the periodic Hello mechanism, in order to gradually develop the values with all other nodes in the network. It also iteratively updates the quantity using the computed values with respect to all its neighbors. The node then uses the Hello mechanism to send the quantity , its end-to-end cumulative path cost to the common destination node- (e.g., node 6 in Figure 1), to all other nodes that are currently connected to node- . This way, each node gets updated about the path costs of all of its direct neighbors' to the common destination node- . The update equation for

(16)

where node- has the minimum among all the current neighbors of node- .

Because of its end-to-end nature, the forwarding rule in DVRPLC is based on the end-to-end cost as opposed to that based on local parameters or as used in UTILITY and PRMPL both of which do not rely on end-to-end cost. The distance vector forwarding rule for a packet from node- to destination node- can be formalized as follows. If node-i is a direct neighbor of node- , forward the packet. Otherwise find node- such that node- has the minimum among all the current neighbors of node- . Then forward the packet to node- only if ; otherwise, continue buffering the node as node- . With this forwarding rule, the forwarding probabilities can be expressed as

(17)

where represents the set of all on-body nodes and where is the set of all neighbors of node- during the th time slot. The forwarding matrix and the delivery probabilities can be computed using (7) and (8), respectively, and finally, the end-to-end packet delay can be computed as using (9).

7.1. Performance Metrics

The primary performance index is the end-to-end Packet Delay(PD), which is modeled in this paper and is attempted to be explicitly minimized by the UTILITY, PRMPL, and DVRPLC protocols as presented in Sections 5.3, 5.4, and 5.5. Unlike in conventional unpartitioned networks, the PD in partitioned on-body networks depends mainly on the storage delay at the intermediate nodes. Two secondary metrics, namely, Packet Hop Count(PHC) and Packet Delivery Ratio(PDR), are also recorded for a more complete understanding. The index PHC captures the number of forwarding per packet delivery, indicating the transmission energy expenditure; it does not indicate the packet delay since the PD in this context depends more on the buffering/storage than on the hop-count.

7.2. Traffic Generation and Data Collection

A chosen source node is programmed to generate data packets at the rate of 1 packet every 4 discrete time slots (each slot is 1.4 sec), with a packet size of 46 bytes. All on-body network nodes are slot-level time-synchronized by the sink node (i.e., node-6 in Figure 1) using periodic synchronization packet broadcast at a high transmission power [23]. By stamping a packet with the transmission time slot-id by the source node and subtracting it from the reception time slot-id at the sink node, it is possible to compute the single-trip packet delay (PD) at the sink node. On its way to the sink node, a data packet collects the entire route information in the form of a list of the intermediate node-IDs. This allows the extraction and analysis of route information including the PHC values.

7.3. Packet Delay (PD)

End-to-end packet delivery delays for a packet from the source node-3 on left upper arm to the sink node-6 on right ankle for all routing protocols analyzed in Section 5 are reported in Figure 9. For each of these protocols, a separate experiment was run for 1320 sec. (i.e., 22 minutes), sending 230 packets, and spanning 6 different body postures and activities (SIT, SIT-RECLINING, LYING-DOWN, STAND, WALK, and RUN), each lasting for 20 sec. Figure 9 reports the average of packet delay computed from the analytical model, on-body experiment, and off-body simulation using network topology traces collected during the on-body experiments. The figure also shows the delay lower-bound obtained by applying the BSDBR benchmark algorithm (presented in Section 6) on the topology traces collected from on-body experiments.

The following observations can be made in Figure 9. First, the experimental, simulation, and model-generated analytical results closely match across all protocols. Second, as a general trend the delay performance improves with the amount of knowledge leveraged on topological locality. Both PRMPL and DVRPLC achieve significantly better delay compared to the other protocols and very close to BSDBR benchmark delay, because they are able to capture multi-scale topological localities in human postural movements using the cost parameters and , as explained in Sections 5.4 and 5.5. The age-based approach UTILITY uses only the short-term locality, which explains its larger delay compared to PRMPL and DVRPLC, but smaller delay than OPPT and RAND, both of which do not leverage any topological locality information and responds based solely on instantaneous link conditions. Randomized forwarding provides slightly better delay since in a typically small WBAN, there are only few possible end-to-end path combinations, leading to quicker delivery than the opportunistic mode in which a delivery is possible only when the source directly meets the destination.

7.4. Packet Hop Count (PHC)

Figure 10 shows the average PHC which serves as an indirect measure for communication energy expenditure (i.e., for transmission and reception) for the on-body sensors. The large number for RAND explains the impacts of random forwarding compared to all other protocols. The protocols DVRPLC and BSDBR take slightly longer routes compared to the other protocols, although those two offer better packet delays. This means that they route packets through better quality links, leading to smaller delays, even though it requires more number of end-to-end hops. Since the opportunistic routing (OPPT) packets are delivered only when a source comes in direct contact of the destination, all packets are delivered with PHC 1.

7.5. Packet Delivery Ratio

Since no link layer packet retransmissions are deployed, the system is not able to recover from the packet drops observed due to the following reason. Due to postural mobility, there are transient blackout periods during which a neighbor may appear to be connected in a node's neighbor table, when in fact it is no longer connected. These blackout periods are created during a node's neighbor time-out period, which was chosen to be two polling frames or 2.8 sec, as reported in Section 3.2. Packet transmissions during such blackout periods end up in packet drops since no link layer reliability is used. All five evaluated protocols suffer from such packet losses, which are captured in the Packet Delivery Ratio (PDR) as reported below.

In Figure 11, the poor PDR for the OPPT protocol is caused due to a very unreliable link between the source and the destination nodes (i.e., nodes 3 and 6 in Figure 1) which are physically situated at two extremes of the subject's body. Since the OPPT protocol relies on direct source-destination contact for packet delivery, the source-destination link quality affects this protocol most. For RAND, since the hop count is large (see Figure 10), it is more likely for a packet to encounter the transient blackout period during its end-to-end trajectory, thus leading to higher drops and low PDs. Lower hop-counts (see Figure 10) for the locality-based protocols, namely, UTILITY, PRPML, and DVRPLC, suffer from fewer drops due to the relatively lower occurrences of the transient blackouts. Note that the concept of such drops do not apply for the Benchmark case and that is why there is no entry for BSDBR in Figure 11.

7.6. Routing Packets from and to Different Body Segments

Delivery delays computed using the developed model and from on-body experiment for packets from different body segments to the sink node placed on the right ankle (i.e., node 6 in Figure 1) are shown in Figure 12. As shown in the figure, the experimental and model-generated analytical results closely match across all protocols. Observe that as the physical distance between a source and the destination increases, the average packet delivery delays for all the protocols increase. Relatively though, all the experimented routing protocols maintain the same trend for the packet delay as observed in Section 7.2 The average packet hop-counts from source nodes 5, 1, and 3 were experimentally logged in the range of 1.25, 1.5, and 2.3, respectively.

Similar trends in the delivery delay were experimentally observed for a large number of other combinations of source and destination nodes placed at different body segments. Although the absolute delay values were different, the overall trend in packet delay follows the same pattern for all such combinations that were experimented with.

7.7. Impacts of Postural Stability

For all the experiments so far, each individual physical posture was made to last for 20 sec. In order to study the impacts of variable postural stability on the routing performance, the subject was instructed to repeat the same sequence of postures as in Section 3, but with different posture durations ranging from 10 sec. to 40 sec.

Figure 13 shows the impacts of posture duration on average packet delay for all five protocols. Due to its significantly higher values, the packet delays for the OPPT protocol are plotted as a separate axis in Figure 13. Observe that the packet delays for all the protocols generally increase with higher posture durations. This is because longer posture duration implies that a connected link remains connected for longer duration and also a disconnected link remains disconnected longer. As a result, a packet that is buffered in a node due to network partitioning remains buffered for longer duration, leading to higher end-to-end delay. In a relative sense, all the experimented protocols maintain the same performance trend for packet delay as observed in Section 3, Figure 9. It should be observed that the packet delays for the protocols UTILITY, PRPML, and DVRPLC maintain very similar difference for a wide range of the posture duration mainly because of the fact that all three of them use the link locality information, leading to the similar trend of variation with posture duration.

7.8. Impacts of Sensor Placements

Additional on-body sensor placements, as shown in Figure 14, were experimented with for evaluating the validity of the routing results obtained so far from the sensor placement shown in Figure 1. Different source and sink nodes are used in the two placement settings P1 and P2 in Figure 14. The inter-posture sequence, described in Section 3.2, was followed by a subject and the corresponding packet delay results are presented in Figure 15 for the placement settings P1 and P2 in Figure 14. Generally, the relative performance trends across all the experimented protocols as observed for the original sensor placement (in Figure 9) remain valid for the new sensor placements P1 and P2 in Figure 14. The delay for placement P1 is larger due to the longer source-to-destination distance compared to that in P2.

Note that the impacts of link failure were not separately studied because the effects of such failures have already been captured via link disconnection in a DTN network. Also, for a given node placement (e.g., Figures 1 and 14), the dynamic postures (e.g., walk and run) and the variability in the posture duration create sufficient amount of dynamism and diversity in the network topologies, leading to a generalized validation of the presented approach.