- Research Article
- Open Access
A QoS-Based Dynamic Queue Length Scheduling Algorithm in Multiantenna Heterogeneous Systems
© N. Zorba and C. Verikoukis. 2010
- Received: 4 January 2009
- Accepted: 30 July 2009
- Published: 25 November 2009
The use of real-time delay-sensitive applications in wireless systems has significantly grown during the last years. Therefore the designers of wireless systems have faced a challenging issue to guarantee the required Quality of Service (QoS). On the other hand, the recent advances and the extensive use of multiple antennas have already been included in several commercial standards, where the multibeam opportunistic transmission beamforming strategies have been proposed to improve the performance of the wireless systems. A cross-layer-based dynamically tuned queue length scheduler is presented in this paper, for the Downlink of multiuser and multiantenna WLAN systems with heterogeneous traffic requirements. To align with modern wireless systems transmission strategies, an opportunistic scheduling algorithm is employed, while a priority to the different traffic classes is applied. A tradeoff between the maximization of the throughput of the system and the guarantee of the maximum allowed delay is obtained. Therefore, the length of the queue is dynamically adjusted to select the appropriate conditions based on the operator requirements.
- Queue Length
- Average Throughput
- Schedule Delay
- Good Channel Condition
- Heterogeneous Traffic
The use of real-time delay-sensitive applications such as voice, video streaming, or online-gaming for indoor WLAN applications has been remarkably growing during the last years. Nevertheless, WLAN was designed as a data transmission technology without the considerations of voice and real-time applications, so that commercial IEEE 802.11 WLAN systems do not guarantee strict Quality of Service (QoS) requirements in terms of maximum allowed delay and/or delay jitter. Moreover, the fact that the wireless environments are characterized by a harsh scenario for communications increases the difficulties to guarantee the desired QoS in WLAN-based systems. The specific characteristics of the wireless channel with multiple undesired effects, such as deep fades and multipath, distort the original information. As a consequence, guarantying QoS by using the scarce available resources in an in-home wireless medium is a challenging aspect for future WLAN systems.
Different QoS metrics are defined and used at different layers of the OSI model . The acceptable signal strength level and/or Bit Error Rate at the receiver may represent the QoS at the physical layer, but at the higher layers, the QoS concepts are quite different as they are usually expressed in terms of minimum-guaranteed throughput, and delay either maximum allowed delay or delay jitter. Different procedures are followed at each layer to fulfil QoS requirements. At DLC layer, QoS is guaranteed by appropriate radio resource management algorithms while at the physical layer other mechanisms such as power control, adaptive coding and modulation, or symbol rate are applied to guarantee the quality of the communications.
It has been proved that the vertical coupling among layers, known as Cross-Layer , can significantly improve the efficiency of the wireless systems. Both theory and experimental evaluations have demonstrated that cross-layer between the physical and the higher layers seem to be unavoidable in wireless environments in order to exploit the wireless channel instantaneous conditions. Such interchange of information not only helps in increasing the system sum rate performance, but also may be used to guarantee the QoS requirements in systems with heterogeneous type of traffic and applications which need different QoS requirements. In general Cross-Layer further advantages can include improvements in terms of link throughput, reduction of the network latency, energy savings in the mobile nodes, or minimization of transmitted power [2, 3].
One of the resources of the system that can be employed to improve the system performance in terms of both rate and QoS is the spatial diversity. The Multiple-Input-Multiple-Output (MIMO) technology in multiuser scenarios shows very interesting results as several users can be simultaneously serviced within the same frequency, time, and codes. Its employment has already been standardized in IEEE 802.11n and IEEE 802.16e, while it is expected to be part of the forthcoming 4th Generation Long-Term Evolution (LTE) Standard. Among the proposed techniques within MIMO, the Multibeam Opportunistic Beamforming (MOB) strategy that has been suggested in  to boost the wireless link capabilities shows the highest performance, lower complexity design, and only partial channel information is required at the transmitter side. MOB can be operated and adopted to fulfil the QoS requirements demanded by the users for their correct operation .
An interesting remark concerning the QoS compliance in commercial wireless systems refers to the outage concept , where due to the wireless channel characteristics, the 100% satisfaction of the strict QoS demands is impossible, for what is known as outage in the QoS requirements . The notion of outage is widely employed by engineers in the cellular systems where commercial systems (e.g., GSM and WCDMA) allow up to 2–5% outage, depending on the scenario and the application. Therefore, the extension of this concept to WLAN-based systems with delay-sensitive applications seems to be the most tractable approach to asset their efficiency.
Taking into consideration all the previous features, the main contribution of this paper is to propose a Dynamic Queue Length in the Data Link Control Layer, in order to guarantee certain QoS, in the Downlink of multiuser and multiantenna WLAN systems with heterogeneous traffic. As a Cross-Layer philosophy is deployed, then the proposed solution considers both the physical and application layers characteristics of the system. To be more precise, the length of the queue depends on the QoS system requirements, in terms of the system throughput and the maximum allowed delay (and jitter) of the most delay-sensitive applications, where some outage is considered in the QoS requirements of these applications.
The paper tackles a multiantenna scenario and chooses the MOB scheme for its transmission strategy.
Through the use of the outage concept, this paper is able to formalize the service distribution characteristics of the MOB scheme, allowing to obtain the minimum rate and maximum scheduling delay in closed form expressions.
An approach to obtain the opportunistic multiuser gain, while providing the system QoS constraints in terms of minimum-guaranteed rate and maximum allowed delay, is presented.
This paper presents a Cross-Layer Dynamic queues management strategy, and studies its performance. A Cross-Layer design is required in order to consider the instantaneous channel conditions and QoS demands.
The rest of the paper is organized as follows. Section 2 makes a review of other similar solutions in the literature and underline their innovation. Section 3 presents the system model while the Multibeam Opportunistic Beamforming (MOB) is introduced in Section 4. Section 5 gives an overview of the system QoS performance followed by Section 6 with the Dynamic Queue Length model. Performance evaluation results are depicted and analysed in Section 7, to close the paper with the future research directions and conclusions in Sections 8 and 9, respectively.
With respect to the aforementioned concepts in a Downlink system with heterogeneous traffic, several proposals in the literature tackle the dynamic queue consideration, but with different objectives and requirements. The authors in  propose a Media Access Control (MAC) protocol for a finite-user slotted channel with multipacket reception (MPR) capability. By adaptively changing the size of the contention class (defined as a subset of users who can access the channel at the same time) according to the traffic load and the channel MPR capability, the proposed dynamic queue protocol provides superior channel efficiency at high traffic load and minimum delay at low traffic load. However, this protocol is dynamic in terms of traffic load queue and does not deal with the problem of having different users with different QoS demands.
An admission control problem for a multiclass single-server queue is considered in . The system serves multiple demand streams, each having a rigid due-date lead time. To meet the due-date constraints, a system manager may reject orders when a backlog of work is judged to be excessive, thereby incurring lost revenues. Nevertheless, in this paper, service classes are turned-away based on predefined load (packets in the queue) thresholds and only the average mean delay is guaranteed, while the maximum delay is not.
A dynamically queuing feature for service enhancement is proposed in , according to the increment of service subscribers and their mobility. In addition, it presents a dynamic queue manager that handles the queue size to increase call completion rates for service enhancements in wireless intelligent network environments. In spite of this, other QoS demands are not possible and the problem of having different users with different QoS demands is not dealt with.
Various QoS requirements of bursty traffic and a dynamic priority queue with two types of traffic are proposed and analyzed in . The system has two separate buffers to accommodate two types of customers, the capacities of the buffers being assumed to be finite for practical applications. But the service order is only determined by the queue length of the first buffer, so that only average QoS demands can be satisfied.
The scheduler gives some buffers and bandwidth to every priority class at every port in . The scheme adapts to changes in traffic conditions, so that when the load changes the system goes through a transient. Therefore, each queue individually carries out its blocking process, which does not provide any tight control on the QoS demands.
We focus on the single cell Downlink channel where receivers, each one of them equipped with a single receiving antenna, are being served by a transmitter at the Base Station (BS) provided with nt transmitting antennas, and supposing that is greater than nt. The considered scenario is actually a multiuser Multiple Input Single Output (MISO) but the results can be easily applied to multiuser MIMO with any receiver processing. This scenario is considered for easiness, as the receiver processing is out of this paper scope, and all main conclusions of the paper are independent of the processing carried out at the receiver. The scenario is identified to be a heterogeneous scenario where users run any of the four different classes of applications. Class 1 represents voice users (the most delay-sensitive application) and has the highest priority, while Class 4 is the lowest priority best-effort class.
It is worth mentioning that the demand of real-time services, such as Voice over IP (VoIP), for strict QoS delay demands, leads to the reconsideration of the ring scattering model , which is widely used in the evaluation of WLAN systems with nonreal time (e.g., data traffic) applications. This is because the QoS requirements have to be satisfied in a tighter time scale, which requires for detailed models to account for the instantaneous channel random fluctuations.
A wireless multiantenna channel is considered between each of the users and the BS, where a quasistatic block fading model is assumed, which keeps constant through the coherence time, and independently changes between consecutive time intervals with independent and identically distributed (i.i.d.) complex Gaussian entries ~ . Therefore, the channel for each user is assumed to be fixed within each fading block (i.e., scenario coherence time) and i.i.d from block to block, so that for the QoS objective, this model captures the instantaneous channel fluctuations in a better approach than the circular rings model. Let be the transmitted vector (as we are in a Downlink scenario), while denote as the th user received signal, given by
where is an additive Gaussian complex noise component with zero mean and . The transmitted signal encloses the independent data symbols to all the selected users with . A total transmitted power constraint is considered, and for ease of notation, time index is dropped whenever possible.
One of the main transmission techniques in multiuser multiantenna scenarios is the MOB scheme , where random beams are generated at the BS to simultaneously serve more than one user. The beam generation follows an orthogonal manner to decrease the interference among the served users, where beams are generated. Within the acquisition step, a known training sequence is transmitted for all the users in the system. Therefore, each user sequentially calculates the Signal-to-Noise Interference Ratio (SNIR) related to each beam, and feeds back to the BS only the best SNIR value together with an integer number indicating the index of the selected beam. The BS scheduler chooses the user with the highest SNIR value for each one of the beams. So, it gets the multiuser gain from the scenario to increase the system throughput. After that, the BS enters the transmission stage and simultaneously transmits to each one of the selected users, where no user can obtain more than one beam at a time.
Since the users with the best channel conditions are selected for transmission, the scheduler is called Opportunistic Scheduler. Therefore, the low complexity MOB strategy achieves high throughput by spatial multiplexing the users with the best channel conditions, making the transmitted signal to enclose the data symbols for the selected users as
This scheme is characterized by its SNIR term due to the interference that each beam generates to its nonintended users, and even though the beams are orthogonally generated, some of the orthogonality is lost in the propagation channel , stating the SNIR formulation for the th user through the th beam as
with as the unit-power beam assigned to the th user, and where a uniform power allocation is considered. As the user with the highest SNIR value is selected for each transmitting beam, then the average system throughput of MOB can be written  as
Although it has been shown that MOB improves the average throughput of the system , the main target of this work is in providing a precise and guaranteed QoS control for all the users, mainly in terms of the maximum allowed delay, and minimum-guaranteed throughput. As it will be later explained, this is achieved through the optimization of the DLC queue length, where the simulations will show an interesting tradeoff between the QoS satisfaction and the system average throughput. It has to be noted that the minimum allowed rate, the maximum allowed delay and the minimum-guaranteed throughput stand as QoS realistic constraints for both real and nonreal time applications, providing the commercial operator with a wider view than the fairness concept, as the QoS is stated in terms of per user exact requirements.
For the consideration of any transmission scheme in commercial standards that run real-time applications, the QoS of the users is a very important aspect that can be characterized by several metrics or indicators based on the design objectives. So, QoS can be expressed in terms of rate, reflecting the minimum required rate per user, or in terms of delay, showing the maximum delay that a user can tolerate for its packets. This paper considers both of the aforementioned QoS concepts, where the proposed transmission scheme guarantees a minimum rate per user, which is presented by a minimum SNIR restriction ( ), through the classical relation , and delivered to it within a maximum tolerable time delay .
As this work deals with real-time applications in WLAN systems, then the QoS demands cannot be satisfied for the 100% of cases due to the channel characteristics. Therefore, some outage in the QoS is accepted , where the outage is currently employed in cellular systems design as GSM and UMTS, and expected in WLAN systems when running real-time applications. As an example, VoIP can accept erroneous packets up to of the total number of packets.
The paper defines two concepts for outage : the scheduling delay outage and the rate outage. The first one is related to the opportunistic access policy and the time instant when the user is provided service. Section 5.1 characterizes the user opportunistic access and obtains the expression for its access delay probability. The second outage concept accounts for the received data rate once the th user is selected for transmission, and whether its rate requirement is satisfied or not. Section 5.2 derives the corresponding SNIR distribution for the selected user and obtains the minimum-guaranteed rate under an outage .
5.1. Access Delay Outage
In TDMA systems (e.g., GSM) each user knows, in advance, its exact access slot; but in an opportunistic scheduler, as a continuous monitorization of the users' channel quality is performed to select the best ones in each slot, then the access to the wireless medium is not guaranteed. Therefore, the study of the access to the channel in the MOB scheme offers several challenges that must be solved for the MOB consideration in practical systems.
This section calculates the maximum access delay from the time that a user's packet is available for transmission at the scheduler until the user is serviced through any of the beams of the BS. If an active user is in the system, but it is not scheduled within its maximum allowed delay (e.g., because its channel conditions are not good enough to be selected by the MOB scheduler), then that user is declared as being in access delay, with an outage probability given by
with as the probability that a maximum of time slots are required to select a user from a group of i.i.d. users (along the paper, all the users are assumed to have the same average channel characteristics, and showing the same distribution for the maximum SNIR value, so that each user has the same probability to be selected. If this is not the case (e.g., heterogeneous users distribution in the cell, with some users far from the BS), then a channel normalization (e.g., division by the path loss) can be accomplished for such a scenario.), where this probability follows a Geometric Distribution  as
In the MOB scheme, each one of the independent users attempts to be serviced by one of the generated beams with therefore from previous equation, the maximum number of time slots until the user is selected for transmission, with a probability of delay outage , is given by
5.2. Minimum Rate Outage
If the BS scheduler selects a user for Downlink transmission, it means that he/she has the maximum SNIR among the users for a specific beam. But the instantaneous channel conditions (i.e., the instantaneous SNIR) may correspond to a transmission rate that does not satisfy its current application rate requirements (e.g., for a predefined Packet Error Rate, the channel can only provide 6 Mbps while the application asks for 24 Mbps). As a consequence, the user is unable to correctly decode the received packets during the current time unit and suffers a rate outage.
Based on the MOB philosophy to deliver service to the users, the serving SNIR value is the maximum SNIR over the active users in the system, corresponding to each generated beam. Using the SNIR equation in (3), note that the numerator follows a Chi-square distribution while the interference terms in the denominator are modeled as , which allows to obtain the SNIR probability distribution function (pdf) as [1, 4]
and the cumulative distribution function (cdf) is then formulated as
and since the serving SNIR is the maximum over all the users' SNIR values (i.e., the opportunistic philosophy), then its cdf is stated as
obtaining the minimum-guaranteed rate, and where is adopted. Equation (13) shows the rate limits of the system, indicating that high requirements induce high outage in the system. Negative values in the right hand term indicate infeasibility of the requested rate. We assume in this paper that the minimum SNIR guarantees successful decoding of packets. Therefore, the following unit step function defines the Packet Success Rate (PSR) related to the as
5.3. Outage of the System
As previously explained, the MOB scheme comes controlled by two different outage measures, but the total system performance has to be defined through a single parameter. Notice that the two discussed kinds of outage are totally independent, as the user's access to the channel happens when its SNIR is the maximum over all the other users, with respect to a given beam, but being the user with largest SNIR does not guarantee that this SNIR is larger than an application predefined threshold . Therefore, the total outage is defined as
standing as the global measure of system outage.
5.4. Maximum Scheduling Delay
In point-to-point scenarios, the queueing delay is the dominant factor in the system delay  while in multiuser systems an additional delay factor is introduced, because the system resources are not all the time available to the same user. We name this additional delay factor as the scheduling delay in multiuser systems. In the round robin systems (e.g., TDMA) the user access to the channel is known in advance, so that its scheduling delay can be easily calculated. However, in opportunistic multiuser systems where the users with the best channel conditions are selected for transmission based on their instantaneous SNIR, a user does not have any guarantee for being scheduled in a specific time, which increases its scheduling delay.
In the context of this paper, we define the maximum scheduling delay as the time period from the instant that a user's packet is available for transmission at the scheduler until the packet is correctly received at its destination. The difference with the access delay definition is the requirement of a rate threshold in order to guarantee the decoding without errors, as in (14). Notice that this definition includes both the delay resulting from the scheduling process (i.e., the opportunistic selection) and the delay caused by the requirements to get a rate above to a minimum required threshold to be correctly received. Therefore, the maximum number of time slots to select a user with a total outage is equal to the access slots (7), defining the maximum allowed scheduling delay.
In order to avoid misleading conclusions for the reader, a brief numerical example is presented. In a scenario with total users, , a system bandwidth of MHz, , required maximum scheduling delay, and Kbps minimum demanded rate for each user, it results that and are obtained. So that the access delay is 25 slots with an access outage of 7.1%. But even though a user is selected, it may get a rate below its requirement with an outage probability of , so that the must be introduced. Therefore, a wireless operator can guarantee to each user, the correct reception of its packet within a maximum scheduling delay of 25 slots and with a total outage of .
As we consider the scheduling delay, both the buffer management and source statistics for arriving packets are not addressed ; the queues stability target  is neither considered. Therefore, we assume a saturated system and only consider the delay resulting from the scheduling process. The total delay (scheduling + queueing) will be tackled as a future work.
5.5. Minimum-Guaranteed Throughput per User and per Slot
Obtaining the system throughput formulation is difficult as several processes are included in the communication procedure. The receiver decoding through the unit step function in (14) simplifies the throughput formulation, as the effects of several steps in the communication process (e.g., coding) are avoided.
In opportunistic multiuser scenarios, the user in not always served by the system, so that its throughput is zero for several time units. Therefore, a normalized minimum-guaranteed throughput per user over the time is required. Notice that such definition of throughput per user and per slot accounts for the user's waiting time and hence, for its corresponding scheduling delay expression. Considering that the bandwidth of the system is , then the minimum-guaranteed throughput per user and per slot is denoted as , in bits, and given as
where the expression in (13) is used to provide a closed form solution for the minimum-guaranteed throughput per user, with all the operating variables. Notice that by increasing the number of users , the minimum-guaranteed rate goes up and as a consequence higher throughput is obtained. On the other hand, larger induces larger scheduling delay, increasing in this way the value of , that drives lower throughput values. This shows a tradeoff on the number of available users in the systems, motivating a control over the value to achieve the system QoS requirements, as will be shown in the next section.
Note that the minimum-guaranteed throughput is the worst case awarded throughput to the users, but it actually defines the throughput value that an operator can guarantee to its customers, obviously, with a given outage ; where the guaranteed throughput per user is different from the concept of average throughput in (4), previously presented. A very common example in commercial systems for average throughput and the minimum-guaranteed throughput is seen in the ADSL service, where, for example, an operator can provide its costumers 20 Mbps (which is the value that appears in its advertisements), while the minimum-guaranteed value for the user is 2 Mbps (National regulatory telecommunication agencies often ask for a guaranteed value of at least 10% of the average value).
At the Physical layer, the WLAN systems use different modulation levels, so that variable transmission rates depending on the channel conditions (measured through the received SNIR) are obtained. The MOB scheme is applied to select the users with the best channel conditions per beam in order to maximize the system average throughput.
Regarding the dynamic queue length mechanism, when the maximum allowed delay (or minimum allowed rate) in the delivery of the most delay sensitive application is smoothly satisfied, then the length of the queue can be increased so that more users can be placed in the DLC layer queue. As a consequence, the MOB scheduler can select the user per beam with the best channel conditions in a bigger pool of choices, increasing in this way the performance of the system in terms of the average throughput in (4). On the other hand, when the maximum allowed delay requirements are hardly satisfied, then the length of the DLC queue is decreased. Therefore, only packets form users within the higher priority classes can be available in the DLC layer queue, so that the MOB scheduler can only select, for each one of the beams, among these users. Likewise, the same procedure can be applied when the minimum-guaranteed throughput per user is the considered QoS indicator.
Note that the proposed dynamic adjustment in the size of the queue shows the tradeoff between the real-time users' QoS demands and the system average throughput in the network, where the best operating point depends on the network operator requirements. It has to be noted that very delay sensitive applications are in general characterized by short packets lengths, such as VoIP, that do not extract all the benefit from the throughput of the system. To find the best operating point, the dynamic queue length (i.e., number of available users at the DLC layer) is maximized, subject to some system requirements in terms of the users' QoS demands. Taking into consideration the existence of outage in the QoS satisfaction, a proposed optimization procedure for the system performance can be stated as
where is the maximum allowed delay and is the minimum required throughput per user and per slot. It is has to be noted that the previous scheme presents the dynamic queue length adjustment together with the QoS concepts (minimum allowed rate, maximum allowed delay, and minimum-guaranteed throughput), where the operator can choose among the QoS demands for the most appropriate ones for each scenario.
The efficiency of our dynamic queue length scheme is compared with a Round Robin-based scheme , where the channel conditions are not taken into consideration in the scheduling process, and the users access to the channel are guaranteed at fixed intervals. This technique is implemented in TDMA-based systems (e.g., GSM) and it has been proved to provide the lowest possible scheduling delay, but the obtained throughput is very low as the channel conditions are not regarded in the scheduling process. Moreover, it can not be combined with the MIMO Multiuser capability, since the application of MIMO Multiuser techniques needs for the users' selection principle to choose users that show the least interference among themselves .
Figure 3 shows how the gap between the two schedulers enlarges as the DLC queue length increases, which is motivated by the MOB performance, where a larger number of users enable a better search for a set of users (2 users in our simulations) that do not interfere a lot among them (i.e., better SNIR value). Also realize that the average throughput gain of MOB is not as amazing as the MOB gain in the outage of the QoS satisfaction, as seen in Figure 2. The explanation for this matter is due to the MOB technique where more users can be serviced (2 users in our study case), so that the users have almost twice the probability to be serviced in comparison with the single user scheduling approach in . But on the other hand, the throughput average gain is not twice due to the interference that the users generate between them. Therefore, we can claim that MOB scheme is more suitable for QoS demands than average throughput performance. This conclusion has not been stated previously in the literature (up to the authors' knowledge), where this result is very interesting for the implementation of MOB (and most probably, for any other MIMO multiuser technique).
This work developed a QoS optimization over the system metrics to guarantee the QoS for the users, but as a future work, a joint optimization over the QoS metrics is also required to avoid any controversial results among them. Moreover, as all current broadband wireless systems are based on the OFDM Access (OFDMA) scheme, a resource management based on the subcarriers allocation is also required to align with current standards.
Another future work is related to the Hour-Aware Resource Management (HA-RMM). As it is defined in the literature, applications running over the different hours have different QoS requirements (e.g., during the night background traffic is the dominant one while during the morning, real-time traffic is needed; where each application has its own QoS demands). Therefore, a smart resource management strategy over the different day hours is desired to achieve a further optimization of the system resources.
A dynamic queue length scheduling strategy has been presented in this work for Downlink multiuser and multiantenna WLAN systems with heterogeneous traffic. Among the users with a packet in their queue, the ones with the best channel conditions are selected for transmission. Through the MOB scheme, the length of the queue defines the maximum achievable average throughput of the system. On the other hand, the QoS requirements of the delay sensitive applications are guaranteed with short DLC queue lengths. A tradeoff appears between the system average throughput and the QoS demands of the users.
The paper proposed a dynamic DLC queue length control, so that the maximum length is allowed to obtain the highest average system throughput, but restricted to the satisfaction of the users QoS. Several alternative QoS measures are presented along the paper and in closed form expressions, so that the wireless operator can choose among them for the most suitable ones for each scenario characteristics and users' QoS requirements.
Besides the dynamic queue proposal, another important outcome of this paper is on how applications and link layers (or in general higher layers) take profit of the advances introduced by multiple antennas and signal processing techniques in the physical layer. A challenge faced by this paper is on how to deal with several aspects from the different layers of the communication process, so that we tried to make the physical layer concepts to be clear for high layers researchers, and vice versa.
This work has been partially funded by the research Projects R2D2 (TSI-020400-2009-72), NEWCOM++ (ICT-216715), and JU-DAR 162.
- Zorba N, Pérez-Neira AI: CAC for multibeam opportunistic schemes in heterogeneous WiMax systems under QoS constraints. Proceedings of the 50th Annual IEEE Global Telecommunications Conference (GLOBECOM '07), November 2007, Washington, DC, USA 4296-4300.Google Scholar
- Shakkottai S, Rappaport TS, Karlsson PC: Cross-layer design for wireless networks. IEEE Communications Magazine 2003, 41(10):74-80. 10.1109/MCOM.2003.1235598View ArticleGoogle Scholar
- Kartsakli E, Cateura A, Alonso L, Alonso-Zarate J, Verikoukis C: Cross-layer enhancement for WLAN systems with heterogeneous traffic based on DQCA. IEEE Communications Magazine 2008, 46(6):60-66.View ArticleGoogle Scholar
- Sharif M, Hassibi B: On the capacity of MIMO broadcast channels with partial side information. IEEE Transactions on Information Theory 2005, 51(2):506-522. 10.1109/TIT.2004.840897MATHMathSciNetView ArticleGoogle Scholar
- Zorba N, Pérez-Neira AI: Opportunistic Grassmannian beamforming for multiuser and multiantenna downlink communications. IEEE Transactions on Wireless Communications 2008, 7(4):1174-1178.View ArticleGoogle Scholar
- Chalise BK, Czylwik A: Robust downlink beamforming based upon outage probability criterion. Proceedings of the 60th IEEE Vehicular Technology Conference (VTC '04), September 2004, Los Angeles, Calif, USA 334-338.Google Scholar
- Zhao Q, Tong L: A dynamic queue MAC protocol for random access channels with multipacket reception. Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, October-November 2000, Pacific Grove, Calif, USA 2: 1235-1239.Google Scholar
- Ata B: Dynamic control of a multiclass queue with thin arrival streams. Operations Research 2006, 54(5):876-892. 10.1287/opre.1060.0308MATHMathSciNetView ArticleGoogle Scholar
- Choi H-O, Kim Y-J, An S, Nam C-K: Dynamic queue management mechanism for service enhancement in wireless intelligent network environment. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '99), December 1999, Rio de Janeiro, Brazil 1:Google Scholar
- Choi DI, Lee Y: Performance analysis of a dynamic priority queue for traffic control of bursty traffic in ATM networks. IEE Proceedings: Communications 2001, 148(3):181-187. 10.1049/ip-com:20010115MathSciNetView ArticleGoogle Scholar
- Hahne EL, Choudhury AK: Dynamic queue length thresholds for multiple loss priorities. IEEE/ACM Transactions on Networking 2002, 10(3):368-380. 10.1109/TNET.2002.1012368View ArticleGoogle Scholar
- Del Prado Pavon J, Choi S: Link adaptation strategy for IEEE 802.11 WLAN via received signal strength measurement. Proceedings of the International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 2: 1108-1113.Google Scholar
- Spiegel MR: Theory and Problems of Probability and Statistics. McGraw-Hill, New York, NY, USA; 1992.Google Scholar
- Neely MJ, Modiano E, Rohrs CE: Dynamic power allocation and routing for time varying wireless networks. IEEE Journal on Selected Areas in Communications 2005, 23(1):89-103.View ArticleGoogle Scholar
- Issariyakul T, Hossain E: Channel-quality-based opportunistic scheduling with ARQ in multi-rate wireless networks: modeling and analysis. IEEE Transactions on Wireless Communications 2006, 5(4):796-806.View ArticleGoogle Scholar
- Knopp R, Humblet PA: Information capacity and power control in single-cell multiuser communications. Proceedings of the IEEE International Conference on Communications, June 1995, Seattle, Wash, USA 1: 331-335.View ArticleGoogle Scholar
- Pubill D, Pérez-Neira AI: Handoff optimization with fuzzy logic in 802.11 networks. Proceedings of the International Symposium on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU '03), September 2006, Paris, FranceGoogle Scholar
- Fu H, Kim DI: Analysis of throughput and fairness with downlink scheduling in WCDMA networks. IEEE Transactions on Wireless Communications 2006, 5(8):2164-2173.View ArticleGoogle Scholar
- Kountouris M, Gesbert D: Robust multi-user opportunistic beamforming for sparse networks. Proceedings of the 6th IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC '05), June 2005, New York, NY, USA 975-979.Google Scholar
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