Performance Analysis of PRMA/DA
in Wireless ATM Network
YuWen Lai
Telecommunication Laboratories, Chunghwa Telecom Co.
Taoyuan, Taiwan 326, ROC
TEL: (03)4245487
EMAIL: ywlai@ms.chttl.com.tw
Abstract
PRMA/DA is a media access control protocol for wireless local area networks (LANs) that is capable of supporting various types of traffic demands, such as constant bitrate (CBR) voice, variable bitrate (VBR) video, and packet data. This protocol, having an air interface comparable to ATM, adopts a dynamic channel allocation scheme which enables expeditious network access and utilizes bandwidth resource efficiently. In this paper, system performance measures, such as throughput and access delay, are evaluated by using a Markov analysis method.
Packet Reservation Multiple Access / Dynamic Allocation (PRMA/DA) [1] is designed to operate in the conventional cellular system architecture. In the cellular architecture, a base station (BS) is located in the center of a radio cell with mobile stations (MSs) dispersed inside the radio cell. Depending on the direction of transmission between the MS and the BS, the communication channel in PRMA/DA is categorized into two separate timeslotted channels: uplink channel and downlink channel. The uplink channel delivers the information from the MSs to the BS, while the downlink channel is used to communicate in the opposite direction. For the uplink transmission, the mobile stations in a radio cell share the communication channel using the PRMA/DA protocol. The downlink channel operates with a contentionfree TDM (timedivision multiplexing) broadcast mode.
PRMA/DA protocol adopts the ATM cell as a fundamental unit of protocol processing and switching in both wired and wireless network segments. The typical structure of the transport cell at the air interface is illustrated in Figure 1. As shown in the figure, the ATM cell is encapsulated by a PRMA/DA header and trailer. The header contains synchronization bits, a NS field indicating the number of slots requested from a mobile station, and other control field. The NS field is of importance to the operation of the protocol, since the field is used to carry the information on the current bandwidth demand of a mobile station to the BS at every frame.
Figure 1 : Cell format at the air interface
PRMA/DA operates on the frame basis. Time on the uplink channel is divided into a contiguous sequence of PRMA/DA frames, which are further subdivided into a fixed number of slots. In particular, a PRMA/DA frame can be segmented into available slots and reservation slots consisting of CBR reservation slots, VBR reservation slots, and ABR reservation slots as illustrated in Figure 2. The BS has absolute in determining the number of both available slots and reservation slots. Furthermore, the BS also specifies the number of slots assigned to each individual reserving station. The number of available slots depends on the intensity of demand to access the network among the mobile stations. In contrast, the number of reservation slots assigned to each reserving station is primarily dependent on the statistical properties of traffic a MS intends to transmit.
Figure 2 : The PRMA/DA frame format
The available slots provide a communication mechanism for a mobile station to attain network access. In order to transport the traffic, an activated station needs to access the network. The network access is made by transmitting a cell in a randomly selected available slot. After completing the contention procedure, the mobile station can use the reservation slots without undergoing further contentions. The contention procedure of the PRMA/DA protocol operates on a random access (slotted ALOHA) scheme. A mobile station, when it has just become active, switches its mode into the contention mode from the inactive mode. A mobile station in the contention mode is called a contending station in PRMA/DA terms. As in the slotted ALOHA, a contending station randomly selects one of the available slots which occupy the beginning portion of a frame and transmits its first cell in that slot. Right after the contention period, the BS advises the contending stations whether the network access is successful or not.
Unless other contending stations try to transmit their cells in the same slot, the mobile station will attain the network access and shift its mode to the reservation mode. If the mobile station fails to acquire the network access due to collision, it needs to repeat the contention procedure at the next frame. The BS broadcasts the new value at the end of each frame. Upon receiving the information, the contending stations prepare for the next contention period. For CBR/VBR traffic, which has stringent timing constraints, the unbounded repetition of the contention procedure is meaningless. Therefore, PRMA/DA protocol specify the maximum time for contention which is called maximum setup time (). If a contention period of a mobile station lasts longer than the maximum setup time, its call will be discarded and the mobile station will return to the inactive mode.
The number of available slots in PRMA/DA varies dynamically depending on the congestion state of the network. As the demand for network access increases, the number of available slots will expand according to the algorithm which will be described later. With decreasing requests for network access, the number of available slots will shrink accordingly. Finally the number of available slots reduces to one when no demand exists.
The number of reservation slots assigned to the reserving stations is governed by dynamic allocation algorithm. The primary factor considered in the algorithm is the statistical properties of the traffic that a mobile station intends to transport. At the connection setup phase, a contending station is required to specify the traffic parameters in the cell that is delegated to contend for an available slot. In the current phase of our work, the statistical properties of the traffic are represented only in terms of the average number () and peak number () of cells generated during a frame period. Further extension will be required to more accurately characterize the traffic. Along with the parameter (), the current bandwidth demand which is delivered by the NS field is considered in determining the number of reservation slots assigned to a reserving station. At the end of each frame, the BS broadcasts the information about the number of reservation slots which have been assigned to each reserving station and the respective slot locations. Upon receiving the information, the reserving stations can begin transmission in their assigned slots in a frame.
1.1 Dynamic Allocation of Reservation Slots
In a mixed traffic environment, each category of traffic, e.g., CBR, VBR, and ABR, has its own unique traffic properties and service requirements to maintain the declared QoS (Quality of Service). In order to enable the dynamic allocation scheme to operate efficiently, the BS requires the following parameters: the average traffic rate (), the peak traffic rate (), and the number of slots requested by a reserving station which is carried in the NS field of a cell.
Once the BS determines the number of available slots (), the rest of the slots in the frame are used to serve the reserving stations as shown in Eq. (1).
where is the total number of slots in a frame and is the total number of reservation slots in a frame.
In PRMA/DA, three categories of traffic, i.e., CBR/VBR/ABR, are prioritized in terms of their respective timing constraints. First, every CBR reserving station, i, takes slots since it has constant bandwidth demand which is equivalent to its traffic parameter . The total number of slots assigned to all CBR reserving stations, , is
where is the set of CBR reserving stations. Second, the total number of ABR reservation slots is
where and is total number of slots requested by the reserving VBR and ABR stations respectively. Third, the total number of VBR reservation slots is
1.2 Dynamic Allocation of Available Slots
The dynamic allocation for the available slots can be formalized as follows:
where is the number of available slots at the (k) th frame, is the number of slots in which collision occurs, and is the number of slots in which successful network access is made.
In this section, we provide performance analysis for the PRMA/DA protocol operating in a mixed voice/video environment and compare it with the simulation results. The analysis parameters are the same as the simulation parameters specified in the paper of PRMA/DA which is proposed by Kim and Widjaja[1]. In their simulation, they do not include the use of VAD (voice activity detector). Thus the CBR stream (64kbps) is generated during the voice call duration. A new voice call arrives at the rate of and the call duration () is exponentially distributed with an average of 3 minutes. During the simulation, Kim and Widjaja fix the number of VBR traffic sources to five which arrive at the beginning of the simulation. The duration of the VBR connection covers the entire simulation. In order to model a VBR video traffic source, they use the video model proposed by Heyman et al.[2]. In the model, the number of cells per video frame is determined by a gamma distribution (or equivalently negative binomial) and a DAR (1) model [2].
It is assumed that a mobile station has infinite buffer capacity. Also an ideal communication channel is assumed, implying that transmission errors and retransmissions do not occur in the simulation. In our analysis, we will follow above assumptions. The analysis parameters are summarized in Table 1.
item 
symbol 
value 
Total number of mobile stations in a single cell 
N 

Frame length (msec) 
6 

Slot length (msec) 
0.06 

Number of slots (cells) per frame 
K 
100 
PRMA/DA channel speed (Kbps) 
R 
7067 
Voice codec data rate (Kbps) 
64 

Duration of a voice packets (msec) 
6.625 

CBR/VBR slot size (bytes) 
53 

Payload of a single slot (bytes) 
48 

Arrival rate (exponential) of new voice calls (call/sec/user) 
0.01~ 0.1 

Average length (exponential) of a voice call (min) 
3 

Maximum (fixed) voice call set up time (sec) 
5 

Video (VBR) frame rate (video frames/sec) 
25 

Average number of cells per video frame 
104.8 

Peak number of cells per video frame 
220 
Table 1 : Performance analysis parameters
2.1 Basic Analysis
In our analysis, we consider a mixed CBR/VBR environment. Since the number of VBR traffic sources is fixed to five and the duration of the VBR connection covers the entire simulation, our analysis will follow this situation and assume that all new arrivals will request CBR services.
2.1.1
Let be the probability of there being n contending stations, a available slots, i available slots in which successful network access is made, and j available slots in which collision occurs. Then
with
where is the number of colliding mobile stations associated with available slot k, and is the number of available slots each of which is associated with l colliding mobile stations.
2.1.2 Estimate of the State Probability Distribution
Let be the probability that a reserving station switches from reservation mode to inactive mode due to the end of a voice call and be the probability that a contending station switches from contention mode to inactive mode because the contention period lasts longer than the maximum call setup time (). Then
Let be the conditional probability that there are exactly A packet arrivals during a frame, given that at the beginning of the frame there were r reserving stations. During time , a reserving station generated either or packets with probability and probability , respectively. For r reserving stations, we have
When the frame length is an exact integer multiple of , i.e., , each reserving station will generate packets during the frame. Therefore is exactly
Now, we consider the queueing model. The system observed at time units of is characterized by a discretetime Markov chain process. The state of this chain is defined by , where a is the total number of available slots, r is the number of reserving stations at the beginning of a frame, and n is the number of contending stations at the beginning of a frame. Let be the transitional probability that the next state will be , given that the present state is .
For
For
where is the dynamic allocation function for the available slots. From Eq. (5), we get
and
The steadystate probability satisfies
The above equations can be solved by using geometric techniques [3] to obtain .
2.2 Throughput
The throughput is as follows.
where
2.3 Access Delay
Let be the probility that each contending station is successfully served during a frame. We get
Let be the average time that a packet waits in the buffer at one contending station until the current frame is over and be the average delay time of a successfully transmitted packet in a frame. We get
So the access delay, AD, is
In our numerical results, the analysis parameters are summarized in Table 1. Figure 3 and Figure 4 show the throughput and CBR access delay, respectively, of PRMA/DA protocol. When the total number of mobile stations in a single cell (N) increases, the throughput increases. However, CBR access delay also increases due to the increase of collision. Mathematical results have shown that PRMA/DA has good throughput and access delay. The trend of mathematical results is similar to the trend of the simulation results in [1].
Figure 3 : Throughput of PRMA/DA protocol
Figure 4 : CBR access delay of PRMA/DA protocol
We have described the method to measure the performance of the PRMA/DA protocol by a discretetime Markov chain process. Mathematical results have shown that PRMA/DA has good throughput and access delay. Until now, we still have some mathematical results under processing. In the future, we will propose more mathematical results to prove that our method is appropriate to analyze PRMA/DA protocol.
References