Modeling and Performance Analysis of MAC Protocol for WBAN with Finite Buffer

Abstract

The IEEE 802.15.6 standard is introduced to satisfy all the requirements for monitoring systems operating in, on, or around the human body. In this paper, analytical models are developed for evaluating the performance of the IEEE 802.15.6 CSMA/CA-based medium access control protocol for wireless body area networks (WBAN) under unsaturation condition. We employ a three-dimensional Markov chain to model the backoff procedure, and an M/G/1/K queuing system to describe the packet queues in the buffer. The throughput and delay performances of WBAN operating in the beacon mode are analyzed in heterogeneous network comprised of different user priorities. Simulation results are included to demonstrate the accuracy of the proposed analytical model.

1. Introduction

Wireless body area network (WBAN) is a novel wireless technology-driven human body monitoring network which aims to predict, diagnose, and monitor the response of the body to treatments[1]-[3]. The network typically consists of a collection of low-power, miniaturized, invasive or non-invasive, lightweight devices with wireless communication capabilities [4]-[6]. The collected data is transmitted to a medical center to be further processed, stored and applied. WBANs must satisfy the various requirements of application scenarios, such as reliability, quality of service (QoS), low power, high data rate and noninterference [7]-[10]. Hence, the IEEE 802.15 working group developed the IEEE 802.15.6 standard optimized for low power devices operating in the vicinity of, or inside a human body (but not limited to humans) [11].

Performance of the CSMA/CA mechanism in IEEE standards has been studied in [12]-[14] for IEEE 802.11, [15], [16] for IEEE 802.11e and [17]-[22] for IEEE 802.15.4. However, there is not much work in the reported literature, which investigates the IEEE 802.15.6-based network performance. In [23], [24], analytical models are presented to estimate the saturation throughput based on a slotted Aloha protocol. In [25], a simple model is proposed to evaluate the theoretical throughput and delay limits of the IEEE 802.15.6-based networks. However, the user priorities and the backoff stages are not taken into account. In [26], [27], analytical models are developed to evaluate performance of the IEEE 802.15.6 CSMA/CA mechanism with respect to exclusive access phase (EAP) and random access phase (RAP), and contention access phase (CAP), but the packet arrival process is not considered, i.e., it is assumed that there is at least one data frame in the queue waiting to be served at all times. Performance of the CSMA/CA mechanism under unsaturation condition is studied in [22] for IEEE 802.15.4, but the developed models are not appropriate for the IEEE 802.15.6 due to the different characteristics of the CSMA mechanisms.

In this paper, we evaluate the performance of the IEEE 802.15.6 CSMA/CA based MAC protocol, and the activities in the contention-free access phases are ignored. We develop a three-dimensional Markov chain to model the backoff procedure of the CSMA/CA mechanism during the exclusive and random access phases of IEEE 802.15.6 under unsaturated condition. The discrete-time Markov chains are solved to calculate the medium access probabilities of all user priorities. Afterwards, we develop an M/G/1/K queuing model to analyze the queue length in the buffer [28]. Using probability generating functions (PGFs), we compute the average packet service time, and furthermore, the average packet delay and throughput are derived. The analytical results are validated by using simulations.

The paper is organized as follows: Section 2 specifies the IEEE 802.15.6 CSMA/CA medium access control, and Section 3 provides a discrete-time Markov chain model for the analysis of the IEEE 802.15.6 CSMA/CA-based MAC for all user priorities. In Section 4, a finite-length first-in-first-out (FIFO) buffer is modeled as an M/G/1/K queue and analyzed by using an embedded Markov chain approach. Section 5 presents the performance analysis, including throughput and average packet delay. Section 6 validates the analytical results by numerical simulations. Finally, we conclude our results in Section 7.

 

2. IEEE 802.15.6 CSMA/CA MAC Specification

In this paper, we assume that the hub in a CSMA/CA-based WBAN operates in beacon mode with superframe boundaries. Each superframe is divide into different access phases as shown in Fig. 1. A hub or any node may obtain contended allocations in RAP if it requires the transmission of data frames for all eight user priorities UPk , k = 0,...,7 , in the WBAN. UP7 has an aggressive priority compared to the other user priorities. During the EAP periods, the medium is only accessible by UP7 with very small contention window sizes. The hub or a node with the highest user priority (UP) frames may treat the combined EAP and RAP as a single EAP to allow continual invocation of CSMA/CA and improve channel utilization.

Fig. 1.IEEE 802.15.6 superframe period for beacon mode

The user priorities, as shown in Table 1, are differentiated by the values of the minimum and maximum contention windows (CWk,min and CWk,max), respectively. Fig. 2 shows the CSMA/CA procedure defined in the IEEE 802.15.6 standard. Based on the CSMA/CA mechanism, a node shall maintain a backoff counter and a contention window to determine when it obtains a new contended allocation. The node sets its backoff counter to a sample of an integer random variable uniformly distributed over the interval [1,CWk]. The node is allowed to transmit one frame of UP over the medium if the backoff counter reaches 0. The contention windows CWk, k = 0,...,7 , are chosen as follows:

Table 1.WBAN user priorities

Fig. 2.CSMA/CA procedure used in IEEE 802.15.6

The node locks the backoff counter when any of the following events occurs:

 

3. Markov Chain Model

In this section, we provide a discrete-time Markov chain model for the analysis of the CSMA/CA-based IEEE 802.15.6 MAC. All eight UPs are considered, and each node has one UP. A node belongs to UPk if it has a queue of user priority k. We consider a single hop WBAN with nk nodes of UPk and lengths of EAP2, RAP2, and CAP are set to 0. Finally, it is assumed that packets arrive at the nodes for transmission according to a Poisson arrival rate of λ packets per packet duration.

The backoff counter for a node of UPk is an integer uniformly drawn over the interval [1, CWk], where CWk = Wk,i, for i = 0,...,m ; m is the transmission retry limit and CWk has minimum value of CWk,min = Wk,0, and maximum value of CWk,max = Wk,mk. CWk is set to CWk,min when the backoff procedure is started. The contention window size during the ith backoff stage for a node of UPk , CWk = Wk,i, is calculated as follows:

Figs. 3 shows the proposed discrete-time Markov chain model of the IEEE 802.15.6 MAC protocol in the unsaturated condition. Let sk(t) and bk(t) represent the backoff stage and the backoff counter corresponding to UPk , respectively. We define pk as the conditional collision probability regardless of the number of retransmission. Let , i = 0,...,m , J = 1,...,Wk,i be the stationary distribution of the chain. In this Markov model, the one-step state transition probabilities are:

Fig. 3.Markov chain of IEEE 802.15.6 for UPk

where gk, k = 0,...,7 are the probabilities that the backoff counter of a node with UPk decreases. Assume that there is sufficient time left for packet transmission, so gk is equal to the probability qk that the medium is idle during backoff countdown, for a node of UPk, k = 0,...,6 , which can be approximated as

For a node of UP7, the probability that the medium is idle during backoff countdown can be described by

where τk is the probability of transmission for a node of UPk assuming that the medium is not busy, pk,a is the probability that a node of UPk has at least one packet to send in a time slot. δ1 and δ2 are expressed as δ1 = lR / (lR + lE), δ2 = lE / (lR + lE), where lR and lE are the lengths of RAP and EAP in slots, respectively. We define Yk, k = 0,...,7 as the input probability to the zero-th backoff phase. Hence, we have

where bidle is the stationary probability of the idle state. By means of relations in (1), and the fact that bk,i,0 = Yk, which can be derived by solving the Markov chain, all the stationary probabilities bk,i,j can be expressed as functions of the values bk,0,0, pk and pk,a

In view of the fact that

we obtain

Use the normalization condition of Markov chain, which means the sum of the stationary probabilities is equal to 1 for k = 0,...,7 , we have

where

where ⎾m / 2⏋ denotes the ceiling function, which is the smallest integer not less than m / 2 . Solving (7) results in the stationary probability of bk,0,0 as the function of pk and pk,a , i.e.,

where

As any transmission starts when the backoff counter is equal to zero, regardless of the backoff stage, the probability τk that a node transmits in a randomly chosen slot can be expressed as

Note that the conditional collision pk is the probability that a transmitted packet encounters a collision, which means, in a time slot, at least one of the remaining nodes transmits. In addition, nodes that do not have the highest priority cannot access the medium during EAP. Thus, for a node of priority UPk, k = 0,...,6 , the conditional collision probability pk during RAP can be expressed as

The conditional collision probability for a node of UP7 is given by

Once pk,a is known, we can obtain the values of τk and pk, k = 0,1,...,7 , from (11)-(13), where pk,a is derived from the following queuing model.

 

4. Markov Queuing Model

A finite-length FIFO buffer is employed at each node, which can be described by the Markov model with a queue capacity K . Note that K means K - 1 packets wait in the queue and one is served, so the buffer length is K - 1. If the buffer is full, the new arriving packets will be dropped. Since the packet generation follows a Poisson distribution and the service time general distribution, thus, it can be modeled as an M/G/1/K queue and analyzed by using an embedded Markov chain approach. The state space of the embedded Markov chain is S = {X0,X1,...,XK}, where Xj, j = 1,...,K , denotes that there are j packets waiting in the queue and that one is served. Particularly, X0 is the state that the queue is empty and no packets are served. Let Bn and Qn be the queue length of the buffer at the beginning and at the end of the nth packet period. Fig. 4 illustrates the Markov model with a queue capacity K . The transition probabilities from one state to another in the transmission process can be expressed as

Fig. 4.Markov model with a queue capacity K

where pac is the probability that the tagged node can catch the medium, which means that either a data packet is successfully transmitted, or a data packet is dropped as the transmission retry limit is reached. Suppose there are N nodes in a fully connected WBAN network. When a tagged node has a data packet to send, the probability that n nodes out of the other N - 1 nodes competing for the medium can be described by

where π0 is the probability that a node have an empty queue in the buffer. Suppose the tagged node randomly choose time slot s to start backoff process, then the probability that it can catch the medium can be written as

where pc,j is the probability that the tagged node suffers a collision during backoff stage j, which means that at least one of the remaining nodes chooses time slot s, s + 1, ..., Wk,j to start backoff procedure, i.e.,

And ps,j is the probability that the tagged node transmits successfully during backoff stage j, which means that the other nodes randomly choose time slots from s + 1, s + 2, ..., Wk,j to start backoff procedure, i.e.,

Using (16)-(18), we obtain

The state transition probabilities of the arrival process are given by:

where Ai is the probability of i packets arriving during (n + 1) -th packet period Ts , i.e., Ai = e-λTs(λTs)i / i!, and A≥i is the probability of no less than i packets arriving in a packet period, i.e., . For simplicity, we define the following probabilities

Given that the queue length is r in the previous packet period, the transition probability that there are l packets in the buffer is denoted by pl,r. By use the fact that , we can obtain the transition probability matrix P = [pl,r](K+1)×(K+1) as follows:

The stationary probability of the number of packets in the buffer at the end of a packet period, denoted by πn , can be expressed as

where 0 ≤ n ≤ K . The stationary probability πn satisfies the following equations

In addition, according to the normalization condition, it follows that

where ∏ is the vector of πn , i.e., ∏ = [π0,π1,...,πK] . Assume that packet arrival information λ , Ai , A≥K are known, solve (19), (24) and (25), we can obtain πj , j = 0,1,..., K . Since π0 is the probability that a node has an empty queue in the buffer, pk,a is derived by

 

5. Performance Analysis

Service time is the time interval from the time instant when a packet becomes the head of the MAC queue to the time instant when the packet is either successfully transmitted or dropped. Consider a system in which each packet is transmitted by means of the RTS-CTS-data-ACK access mechanism. Let St(z) be the PGF of the packet transmission time, and Ct(z) be the PGF of transmission time due to an RTS collision, which are described by

where rts/cts denotes the length of RTS/CTS packet, and ack the length of ACK packet. sifs is the time duration of inter-frame space (SIFS), and ld is the average packet length. We assume that all values of length are in time slots.

The PGF of the time that the backoff counter decrements by one during the backoff stage i can be expressed as

Further, we can obtain the PGF of the time consumed in the backoff stage i, i.e.,

Since the service time is composed of the backoff time and the transmission time, and the probability that the packet is successfully transmitted at the uth backoff stage is , we can obtain the PGF of the service time

Thus, the average service time can be calculated by

The packet delay is composed of two parts. One is the service time computed in the above, and the other is the queuing time from the time instant when a packet arrives in the queue to the time instant when it becomes the head of the queue. Let be the steady-state probability that there are j packets found by an arbitrary arrival, which can be evaluated in terms of the steady probability that a departure customer leaves behind j customers, i.e., πj . This leads to the expressions for the values of

The mean packet number in the buffer is straight forward

Based on Little's law, the mean queuing delay is derived by

Since the average packet delay is the sum of the average service time and average queuing delay, it follows that

Based on the backoff algorithm and queuing model, per class throughput is computed by

where E[Pck] is the average packet payload size. The system throughput can be obtained as

where ρk = nk / N is the probability of UPk in the system.

 

6. Simulations

To validate the analytical model, simulation results are obtained by a significant amount of iterations. In this section, we investigate the performance analysis of the throughput and packet delay for different user priorities under the unsaturation and saturation conditions. We choose three classes of user priorities, i.e., a lower priority class UP0 , a medium priority class UP3 , and a higher priority class UP5 to explain the results. And three pairs for (τk, pk) in numerical values are obtained from the associated system of non-linear equations. The throughput and packet delay results are produced considering equal numbers of nodes for each user class.

Table 2.Simulation parameters

Figs. 5 and Figs. 6 show the average throughput and packet delay of WBAN nodes with varying packet arrival rates λ for different user priorities, respectively. It can be seen that the higher priority nodes achieve higher throughput compared to the lower priority nodes. As the packet arrival rate in the network increases, the higher priority nodes access channel more frequently due to the lower CWmin and CWmax values, compared to the lower priority ones. In addition, given λ, the packet delay with the lower priority nodes is longer than the nodes with relative high priorities. With the arrival rate rising, the packet delay increases, and arrives at the peak value when the network approaches the saturated condition.

Fig. 5.Average throughput under the unsaturation condition

Fig. 6.Average packet delay under the unsaturation condition╲

Fig.s 7 and Figs. 8 illustrate the average throughput and packet delay of WBAN nodes for different user priorities in the saturation condition. As shown in Fig. 7, for the nodes with the same priority, the throughput decreases with the increasing of the number of nodes in the network because contentions will occur more frequently. When different priorities are assigned to the nodes, the higher priority class (UP5) with lower contention window values can obtain a contended allocation more frequently than the lower priority class, UP0. Hence, the nodes with the higher priority class achieve higher throughput with respect to the lower priority nodes. The performance of the average packet delay is shown in Fig. 8, obviously, as the use priority decreases, the packet delay becomes much longer. In addition, the packet delay increases with the number of the nodes, and the differences between different priority classes are greater for the larger amount of nodes.

Fig. 7.Average throughput under the saturation condition

Fig. 8.Average packet delay under the saturation condition

 

7. Conclusions

In this paper, we evaluate the performance of the CSMA/CA based medium access mechanism of IEEE 802.15.6 under the unsaturation condition. The discrete-time Markov chains are used to solve the random medium access probabilities of all user priorities. A finite-length FIFO buffer is modeled as an M/G/1/K queue and analyzed by using an embedded Markov chain approach. Further, the throughput and average packet delay of WBANs are derived in heterogeneous networks. Simulations are carried out for different user priorities under the unsaturation and saturation conditions. Simulation results indicate that both the packet arrival rate and the user priorities have a great influence on the average throughput and packet delay of WBANs.