Radio resource reservation for heterogeneous traffic in cellular networks with spectrum leasing
 ShowShiow Tzeng^{1}Email author,
 YingJen Lin^{2} and
 YuChing Hsu^{3}
https://doi.org/10.1186/168714992012206
© Tzeng et al.; licensee Springer. 2012
Received: 22 August 2011
Accepted: 27 May 2012
Published: 2 July 2012
Abstract
Radio channel reservation is used to alleviate call dropping which may occur in two situations: (i) handoff between cells in cellular networks, and (ii) channel withdrawal in wireless networks with spectrum leasing. In this article, we study a radio resource reservation scheme for heterogeneous traffic in a cellular network with spectrum leasing, in which one reservation pool is used to alleviate the two types of call droppings. Since different types of traffic have different tolerances to the exhaustion of channels, it is critical for different types of traffic to select the optimal size of the reservation pool such that the channel requirements of different types of traffic are satisfied while throughput is maximized. A threedimensional Markov chain is presented to find the optimal size of reservation pool. Numerical and simulation results show that (i) the selected parameters of reservation satisfy the qualityofservice requirements of different types of traffic while produce high throughput, and (ii) channel withdrawal yields higher impact on realtime traffic than nonrealtime traffic in terms of throughput.
Keywords
Introduction
Radio resource is scarce and precious; however, radio spectrum is underutilized in most wireless systems in which radio spectrum is statically assigned[1]. One possible way to efficiently utilize the radio spectrum is to allow spectrum sharing between various wireless systems[2–6]. One wireless system can lease radio spectrum from (or out to) another wireless system. Then, mobile users in one system can dynamically access radio channels in another one. In such an environment, a system that leases out its radio channels to another always has the first priority to use its radio channels; that is, the system can withdraw its radio channels from another when the system requires the radio channels.
An ongoing call may be dropped by channel withdrawal. When a channel is forcibly withdrawn from a mobile user, the mobile user releases the withdrawn channel and attempts to handoff to another idle channel in order to continue its communication. If no free channel is available to the mobile user, the user is dropped; otherwise, the user continues its communication. The probability that a handoff user due to channel withdrawal is dropped is called withdrawal dropping probability herein. To reduce the call dropping, a number of channels are reserved for the calls suffering channel withdrawal[7].
Cellular wireless networks are a category of widelydeployed wireless systems, in which service areas consist of cells. In such a wireless network, mobile users may move from one cell to another. When a mobile user moves from a cell to a neighbor cell, a intercell handoff procedure is initiated to continue the mobile user’s communication. If free channels in the neighbor cell are insufficient to satisfy the channel requirement of the mobile user, the mobile user is dropped. The probability that an intercell handoff attempt fails is referred to as intercell handoff dropping probability in this article. From the viewpoint of mobile users, the intercell handoff dropping probability should be as low as possible. To provide mobile users with low intercell handoff dropping probability, threshold based channel reservation schemes have been presented in[8, 9].
This article considers a cellular network which can lease a spectrum band from another wireless system; in such a network, traffic congestion can be alleviated by using spectrum leasing. As mentioned in previous paragraphs, channel reservations have been separately reserved for the two types of call dropping which respectively result from channel withdrawal and intercell handoff. Due to the gain of resource sharing[10], the two reservations can be implicitly combined into a reservation pool[11]. However, the optimal reservation in the pool is not the sum of the two optimal reservations in[7, 8], which reasons are as follows. First, the optimal reservation in[8] is found in cells with fixed channels, but the cells considered herein have variable channels due to channel leasing and withdrawal, which complicates the channel reservation for intercell handoff calls. Second, the optimal reservation in[7] is found in an environment without intercell handoff call arrivals, but the cellular network herein includes the intercell handoff arrivals, which worsens the negative effect of channel withdrawal. Third, due to resource sharing, fewer channels are possibly reserved to keep the same level of dropping probability for the two types of call dropping. In summary, the penalty for the resource sharing gain is to increase the complexity of selecting the optimal number of reservation channels.
The selection of optimal reservation in the pool is further complicated for heterogeneous traffic which includes realtime and nonrealtime traffic, because realtime and nonrealtime traffics have different tolerances to the exhaustion of channels. Nonrealtime traffic is moderately sensitive or insensitive to the exhaustion of channels; that is, when a channel is forcibly withdrawn from a nonrealtime user, the nonrealtime user can be temporarily placed into a queue to wait a free channel in order to resume its communication. On the contrary, realtime traffic is sensitive to the exhaustion of channels; when a channel is forcibly withdrawn from a realtime user, the realtime user is dropped if no free channel is available to the realtime user.

the withdrawal dropping probabilities of realtime and nonrealtime calls are guaranteed,

the intercell handoff dropping probabilities of realtime and nonrealtime calls are kept below a certain level,

the queuing (or waiting) time of nonrealtime calls in a cell is guaranteed,

the throughput (i.e. the completed calls per time unit) is maximized.
In this article, we present a thresholdbased channel reservation scheme, which reserves channels in a single pool, for realtime and nonrealtime traffic. A threedimensional Markov chain is developed to describe the system state of the channel reservation in a cellular wireless network with spectrum leasing. Based on the Markov chain, we calculate the desired qualityofservice metrics (in terms of the intercell handoff dropping probability, withdrawal dropping probability and waiting time) and throughput. Then, given two thresholds for realtime and nonrealtime traffic, we can apply our analyses to calculate the corresponding qualityofservices and throughput. Therefore, we can select optimal thresholds from a wide range of combinations of different thresholds for the thresholdbased channel reservation such that the qualityofservices of mobile users are satisfied while throughput is maximized. Numerical and simulation results show that, the selected thresholds can guarantee the qualityofservice requirements of realtime and nonrealtime traffic while produce high throughput.
The rest of this article is organized as follows. Section “Channel reservation in an environment of spectrum leasing” describes the thresholdbased channel reservation in a cellular network with spectrum leasing. Section “Numerical analyses” describes our numerical analyses of the channel reservation scheme. Subsequently, performance evaluation is described in Section “Performance evaluation”. Finally, some concluding remarks are presented in Section “Conclusions”.
Channel reservation in an environment of spectrum leasing
In this section, we first describe a cellular environment of spectrum leasing. Then, in such an environment, we describe a threshold based channel reservation scheme for realtime and nonrealtime traffic.
The environment of spectrum leasing
A cellular wireless network may be licensed for holding a radio spectrum over a long period of time. The licensed radio spectrum can be further divided into radio channels. The licensed radio channels in a cellular wireless network are called “licensed channels” herein. After mobile users register in a cellular wireless network, the mobile users can use the licensed channels in the cellular wireless network. In addition, when the mobile users are using the licensed channels in the cellular wireless network, the cellular network does not forcibly withdraw the licensed channels from the mobile users. Although a mobile user may request one or more channels, we assume, for simplicity, that a mobile user merely requires one channel in this article.
A cellular wireless network can lease its licensed channels out to another wireless network. In this article, a wireless network that leases out its licensed channels is referred to as “channel licensee”. A cellular network that leases radio channels from a channel licensee is referred to as “channel leaseholder”. For a channel leaseholder, the radio channels that are leased from a channel licensee are called “leasehold channels”. In a channel leaseholder, a leasehold channel can be allocated to a mobile user that registers in the channel leaseholder.
A leasehold channel in a channel leaseholder will be withdrawn when the channel licensee of the channel requires the channel. If this channel withdrawal occurs, the mobile user which is using the leasehold channel will perform handoffs between different spectrums that will be described in the following subsection. Besides, the channel is held and used by the channel licensee of the channel. When the channel licensee releases the channel, the channel becomes free and is available to the channel leaseholder of the channel.
In this article, we consider a cellular wireless network which can lease channels from another wireless network. In the network, there are licensed channels and leasehold channels in a cell. Due to channel withdrawal, the channels available to mobile users in a cell are the licensed channels in the cell plus the leasehold channels which are not withdrawn in the cell. Note that the licensed channels in a cell could be leasehold channels in cells on another network. Since the cell has the first priority to use the licensed channels, the cell could withdraw the license channels that are used by the cells on another network, which can be regarded as that the licensed channels, which are used or not used by another network, are always available to the cell. Therefore, the scenario that the licensed channels in a cell are leased out to the cells on another network is implicitly included in our considered environment.
Threshold based channel reservation
Two thresholds T_{ r } and T_{ n } are separately used to prevent new realtime and nonrealtime mobile users from entering a congested cell to consume a free channel, worsen a congested situation and degrade qualityofservices. The thresholds are applied to new mobile users but are not applied to those ongoing mobile users suffering intercell handoff or channel withdrawal. In other words, the thresholds reserve a number of free channels for those ongoing mobile users to continue their communications. Under such a threshold based reservation architecture, call admission, intercell handoff and channel withdrawal procedures are described in detail as follows.
Call admission procedure
Intercell handoff procedure

Since nonrealtime users are insensitive to transmission delay, nonrealtime users can tolerate pauses in data transmission. When there is no free channel in a cell, a nonrealtime intercell handoff call can be placed into a queue to wait for a free channel. If there is at least one free room in the queue, the nonrealtime intercell handoff call is placed into the queue; otherwise, the intercell handoff call is dropped.

If the intercell handoff call is realtime, the following two conditions are checked: (i) whether one or more nonrealtime users are using channels in the cell and (ii) whether the number of nonrealtime users in a queue is less than C_{ q }, where C_{ q }is the maximum number of mobile users which can be accommodated in the queue. If the two conditions are satisfied, one of the nonrealtime users which are using channels is randomly selected, interrupted and placed into a queue; then, the channel occupied by the nonrealtime user is released to the realtime intercell handoff call. Otherwise, the realtime intercell handoff call is dropped.
Channel withdrawal procedure
When a withdrawal channel is released from a channel licensee, the channel is available to mobile users in a cell in a channel leaseholder. Moreover, when a mobile user completes its communication in a cell or moves out of a cell, a busy channel which is allocated to the mobile user is released and is also available to other mobile users in the cell. If there is at least one nonrealtime user in a queue in a cell at the instant time of channel release, the channel will be allocated to a nonrealtime user which is selected from the queue in a firstcomefirstserve manner.
Numerical analyses
In this section, we first describe the assumptions used in our analyses. Then, we give an example to explain a threedimensional Markov chain which is used to analyze the performance of the threshold based reservation scheme. In order to formally express the global balance equations of the Markov chain, nine indicator functions are defined; then, an iterative procedure is introduced to solve the global balance equations. Finally, we derive the performance and qualityofservice metrics of the threshold based reservation scheme, and an procedure is introduced to obtain the performance metrics.
Assumptions
For tractable analysis and low computation complexity[12], we consider a cellular wireless system with homogeneous cells in this article. The radio channels in the cellular wireless network consist of licensed channels and leasehold channels. The total number of licensed channels in a cell is fixed and denoted by C_{ i }; the maximum number of leasehold channels in a cell is fixed and denoted by C_{ e }. Then, the maximum number of channels available in a cell, which is denoted by C, is equal to C_{ i } + C_{ e }.
New mobile users arrive at a cell according to a Poisson process with mean rate λ. Let p_{ r } be the probability that a new arrival is a realtime user. Then the probability that a new arrival is a nonrealtime user is 1−p_{ r }. Let λ_{r, n} and λ_{n, n}be respectively the new arrival rates of realtime users and nonrealtime users at a cell. Then, λ_{r, n}=λ_{ p r }, and λ_{n, n}=λ(1− p_{ r }). The lifetimes of a realtime call and a nonrealtime call are exponentially distributed with means${\mu}_{r,n}^{1}$ and${\mu}_{n,n}^{1}$. The arrival of intercell handoff users into a cell is assumed to be a Poisson process. The mean rates of realtime and nonrealtime intercell handoffs are respectively denoted by λ_{r, h} and λ_{n, h}, and the values of λ_{r, h}and λ_{n, h} are α λ_{r, n} and β λ_{n, n}, where α>0 and β>0. The durations that a realtime user and a nonrealtime user stay in a cell are exponentially distributed with means${\mu}_{r,h}^{1}$ and${\mu}_{n,h}^{1}$ respectively. We assume that the arrival of channel withdrawals is a Poisson process with mean rate λ_{ w }. The duration that leasehold channels are withdrawn is exponentially distributed with mean${\mu}_{w}^{1}$.
The Markov chain for the threshold based channel reservation

The transition rates from state (1,2,0) to states (1,1,1) and (0,2,1) are 0.5 ?_{ w }because a leasehold channel is randomly withdrawn from a being served realtime user or a being served nonrealtime user in state (1,2,0).

The transition rate from state (0,1,0) to state (0,2,0) is ?_{n, h}because new nonrealtime users are blocked due to the threshold T_{ n }=1; similar phenomena also appear in states (i,j,k), where j=1.

The transition rate from state (1,0,0) to state (2,0,0) is ?_{r, h}; this is because new nonrealtime users are blocked due to the threshold T_{ r }=1; similar phenomena are also in states (i, j, k), where i=1.

The transition rate from state (0,3,0) to state (0,2,0) is 2 µ_{n, n} + 3µ_{n, h}. Since two nonrealtime users are being served in state (0,3,0), the rate at which nonrealtime users complete their communication is equal to 2 µ_{n, n}. Due to the mobility of mobile users, the rate at which mobile users handoff to neighbor cells in state (0,3,0) is 3 µ_{n, h}. Therefore, the total departure rate in state (0,3,0) is 2 µ_{n, n} + 3µ_{n, h}.
From the Markov chain in Figure4, we can easily write down its corresponding global balance equations which general form is formally and concisely expressed in the Equation (10). Before concisely expressing the general form of the global balance equations of the Markov chain for the threshold based reservation scheme, we first define nine indicator functions.
Indicator functions
To concisely present the balance equations, we first define an eligible state and nine indicator functions. A state (i, j, k) is eligible if the following four conditions are satisfied, i.e. 0≤ i≤ C, 0≤ j≤ C + C_{ q }, 0≤k≤ C_{ e } and 0≤i + j + k≤ C + C_{ q }. Given an eligible state (i, j, k), the nine indicator functions are described as follows.
Global balance equations
Performance metrics
We use the equilibrium probabilities of the Markov chain of the threshold based channel reservation scheme to calculate performance metrics as follows.
Intercell handoff dropping probability
Withdrawal dropping probability
Mean waiting time
Throughput
Calculate performance metrics
 (1)
Give initial values for p(0,0,0) and p(1,0,0), and set P _{r, cd}and P _{n, cd}to be zero.
 (2)
Use Equation (10) to calculate p( i, j, k) for all eligible states ( i, j, k).
 (3)
 (4)
If (i) the different of the new P _{r, cd}and the P _{r, cd}in the previous iteration and (ii) the different of the new P _{n, cd}and the P _{n, cd}in the previous iteration are less than a small value ∊, the procedure is terminated. Otherwise, go to step 2.
The value of ∊ at Step 4 in the above procedure is selected to be 10^{−3}. The iterative procedure converges, and we can obtain the equilibrium probabilities of eligible states, and use the equilibrium probabilities to calculate the remaining performance metrics in Equations (16)–(20).
Performance evaluation
In this section, we first verify numerical results by simulations. Then, we use an example to explain that the selected thresholds are optimal thresholds which satisfy the qualityofservice requirement while produce maximum throughput. Finally, we study the performances of realtime and nonrealtime traffic at different loads with various withdrawal ratios. The parameters commonly used in the section are described as follows. The number of licensed channels in a cell, C_{ i }, is 6. The maximum number of leasehold channels in a cell, C_{ e }, is equal to 24. The mean lifetimes of realtime and nonrealtime users,${\mu}_{r,n}^{1}$ and${\mu}_{n,n}^{1}$, are equal to 120 s. The mean durations that realtime and nonrealtime users sojourn in a cell,${\mu}_{r,h}^{1}$ and${\mu}_{n,h}^{1}$, are equal to 60 s. The mean duration that leasehold channels are withdrawn,${\mu}_{w}^{1}$, is equal to 120 s. The maximum number of calls which can be accommodated in a queue, C_{ q }, is equal to 3. The probability that new mobile users are realtime users, p_{ r }, is equal to 0.6. The withdrawal ratio γ is defined as the ratio of the mean number of withdrawal channels to the total number of leasehold channels in a cell. In this article, the Erlang load per channel is defined as the ratio of the new call arrival rate in a cell to the product of the mean number of available channels in a cell and the mean service rate of mobile users; that is, the Erlang load per channel is equal to$\lambda /\left(\stackrel{\u0304}{C}\stackrel{\u0304}{\mu}\right)$, where$\stackrel{\u0304}{C}={C}_{i}+(1\gamma ){C}_{e}$ and$\stackrel{\u0304}{\mu}={p}_{r}{\mu}_{r,n}+(1{p}_{r}){\mu}_{n,n}$. The handoff rates of realtime and nonrealtime users are two times the new call arrival rates of realtime and nonrealtime users.
Analysis and simulation results
Performance metrics  Analysis  Simulation  

New call blocking probability  Realtime  0.28  0.29 
Nonrealtime  0.28  0.29  
Intercell handoff dropping probability  Realtime  0.035  0.036 
Nonrealtime  0.035  0.036  
Withdrawal dropping probability  Realtime  0.044  0.045 
Nonrealtime  0.033  0.034  
Queuing time (s.)  Nonrealtime  1.23  1.24 
Realtime  0.53  0.53  
Throughput (Erlang)  Nonrealtime  0.35  0.34 
Total  0.88  0.87 
Comparison of QoS and throughput between optimal and nonoptimal thresholds
Nonoptimal thresholds  Optimal thresholds  

Performance metrics  T_{ r }=14, T_{ n }=30  T_{ r }=12, T_{ n }=30  T_{ r }=13, T_{ n }=30  
Intercell handoff dropping probability  Realtime  0.028  0.024  0.026  
Nonrealtime  0.028  0.024  0.026  
Withdrawal dropping probability  Realtime  0.037  0.032  0.034  
Nonrealtime  0.029  0.025  0.027  
Queuing time (s.)  Nonrealtime  1.06  0.93  1.00  
Realtime  0.50  0.47  0.48  
Throughput (Erlang)  Nonrealtime  0.36  0.37  0.37  
Total  0.86  0.84  0.85 
Cognitive networks may suffer different withdrawal ratios which may result in different system performances. In the following, we consider two withdrawal ratios, 0.4 and 0.8, in a cognitive network where the length of queue is 5. The QoS requirement of queuing time is 5 seconds, and the remaining QoS requirements are 0.04. The optimal values of the admission thresholds T_{ r } and T_{ n } are 7 and 30 at γ=0.8; the optimal values of T_{ r }and T_{ n } at γ=0.4 are 30 and 30.

The qualityofservice metrics at different withdrawal ratios satisfy our objective; that is, (i) the intercell handoff and withdrawal dropping probabilities of realtime and nonrealtime users are kept below 0.04, and (ii) the waiting time of nonrealtime users are below 5 seconds.

Nonrealtime users produce lower intercell handoff and withdrawal dropping probabilities than realtime users, because nonrealtime users can be placed into a queue when channels are exhausted.
Conclusions
Radio channel reservation is critical to provide qualityofservices for heterogeneous traffic in a cellular network which leases radio channels from another wireless networks. In such a network, we present a thresholdbased channel reservation, which reserves channels in a single pool, for heterogeneous traffic, i.e. realtime and nonrealtime traffic. We first develop a threedimensional Markov chain to describe the system state of the thresholdbased channel reservation in the network and present formal equilibrium equations of the Markov chain. Next, based on the Markov chain, we further derive the desired qualityofservice metrics (in terms of channel withdrawal dropping probability, intercell handoff dropping probability, mean waiting time) and throughput. Then, given two thresholds for realtime and nonrealtime traffic, we can apply our analyses to calculate the corresponding qualityofservices and throughput. Therefore, we can select optimal thresholds from a wide range of combinations of different thresholds such that the qualityofservices of mobile users are satisfied while throughput is maximized. Numerical results show that, the selected thresholds can guarantee the qualityofservice requirements of realtime and nonrealtime traffic at different situations of channel withdrawal and produce high throughput.
Methods
The numerical analysis of the Markov chain model in this paper is conducted by using C programs. The simulations, which are used to verified the numerical analysis in this paper, are conducted by discrete event driven simulation with C programs.
Declarations
Acknowledgements
This research was partially supported by the National Science Council, Taiwan, under grants NSC 1002221E017007 and NSC 1012221E017 011.
Authors’ Affiliations
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