performance evaluation of a request-tdma/cdma protocol ... - CiteSeerX

Journal of Inter onne tion Networks, Vol. 2, No. 1 (2001) 49-67

fWorld S ienti Publishing Company

PERFORMANCE EVALUATION OF A REQUEST-TDMA/CDMA PROTOCOL FOR WIRELESS NETWORKS

MAINAK CHATTERJEE and SAJAL K. DAS Center for Resear h in Wireless Mobility and Networking (CReWMaN) Department of Computer S ien e and Engineering University of Texas at Arlington Arlington, TX 76019-0015

Re eived February 5, 2000 Revised January 27, 2001 This paper proposes a new medium a

ess ontrol (MAC) proto ol, alled RequestTDMA/CDMA, for supporting multimedia traÆ in wireless networks. In this hybrid proto ol, CDMA ( ode division multiple a

ess) is laid over TDMA (time division multiple a

ess), where a time frame has two kinds of slots, namely data slots and ontrol slots. The data slots are used to the user to transmit their data while the ontrol slot holds the information for the next frame's slot allo ation. Ea h data slot in a frame an be simultaneously used by multiple users with the help of uniquely assigned odes. Whenever a user needs to transmit a message, he rst sends a request message to the entral ontroller and enters the ontention pro ess. The ontroller takes into onsideration the time of generation of a all, the bit rate requirement and the message length while reserving slots for the entire length of the message generated. The user then goes into the transmission phase if he is su

essful in the ontention pro ess, and ontinues to transmit his data till the entire message is sent. Three s heduling algorithms for the allo ation of data slots are proposed and their performan e are studied for four lasses of traÆ . We also analyze our proto ol using a two-dimensional Markov hain model, and ompute the state transition probabilities and derive the average waiting time for a given system load. By simulation experiments we show that our request-TDMA/CDMA proto ol is able to ee tively ombine the orthogonality of both time and ode division multiplexing. Further enhan ements are also proposed to de rease the waiting time and in rease the average hannel utilization. Keywords:

Hybrid proto ol, resour e allo ation, TDMA, CDMA.

49

50

Request-TDMA/CDMA Proto ol

1. Introdu tion

In the past two de ades there has been a tremendous growth in the eld of wireless

ommuni ations. The ultimate goal is to provide ommuni ation servi es anywhere, anytime using light-weight portable devi es at a minimum ost with a

eptable delay, quality and se urity. To provide servi e to a devi e whi h is mobile, it is essential that the devi e is onne ted to a trans eiver. These trans eivers are the base stations in a typi al ellular infrastru ture, where the overage area is divided into ells. Ea h ell is served by a base station and the base stations are onne ted to the base station ontroller (BSC) through a high bandwidth line whi h is in turn

onne ted to the mobile swit hing enter (MSC). The bottlene k in these types of networks is the hannel bandwidth between the mobile devi e and the base station. The bandwidth is just enough to sustain a full-duplex voi e ommuni ation. Also, these hannels are prone to noise resulting in high bit error rate. Due to the s ar ity of the wireless hannel bandwidth, it is essential that the available bandwidth is used as mu h as possible. More re ently, there has been a growing interest to provide wireless a

ess to appli ations that are typi ally of lo al area networks giving rise to the on ept of wireless LANs (WLAN) 8 . With the advent of high bandwidth wireless networks, various kinds of multimedia traÆ { text, voi e, audio and video { are expe ted to be supported. Multimedia appli ations are hara terized by quality-of-servi e (QoS) parameters su h as bit rate (bandwidth), delay and jitter requirements 13 . The available bandwidth to a wireless system is limited and must support a mixture of real time and non-real time appli ations. Moreover, the dynami nature of the wireless medium makes it diÆ ult to guarantee the users of a ell to have good propagation onditions all the time. In a multimedia environment the real-time appli ations generally have higher priority than the non-real time traÆ , and hen e they are allo ated a signi ant portion of the bandwidth. Whenever there are more than one independent user, trying to a

ess the same resour e at the same time,

on i ts an o

ur resulting in orruption of data pa kets of all the ontending users. It is not always possible to allo ate resour es to individual users be ause the resour e is not only s ar e but also expensive. Sin e sharing the limited radio spe trum resour e is a ommon phenomenon in wireless networks, a need for medium a

ess ontrol (MAC) proto ol arises. One of the main onsiderations in the design of a wireless system is to in orporate multiple a

ess s hemes 4 that make eÆ ient use of the allo ated bandwidth. Most of the known wireless MAC proto ols are not spe i ally designed to support multimedia appli ations. Sometimes a se ond proto ol is used on top of the existing MAC proto ol to support su h appli ations su

essfully with proper QoS requirements. Sin e a single proto ol annot often handle the throughput and laten y demands, hybrid proto ols 1;5;14 are designed whi h ombines the features of more than one proto ols and thus perform better. The ellular radio apa ity using spe ial multiple a

ess s hemes has been studied 6 . Multiple a

ess s hemes having at least ode division multiple a

ess (CDMA) or


51

spread spe trum multiple a

ess (SSMA) omponent are superior to other multiple a

ess s hemes be ause by these te hniques, the frequen y sele tivity of the radio

hannel, whi h severely impairs the system performan e, an be averaged out 7 . In this paper we propose a request-TDMA/CDMA proto ol for supporting multimedia traÆ in wireless networks, a preliminary version of whi h an be found in 3 . Our proto ol is a ombination of xed and random assignments of hannel resour es for supporting traÆ with various data rates. This proto ol an be used as a multiple a

ess s heme within one ell of a ellular network. The resour es are managed by the base station (s heduler) and are allo ated to the users based on

ertain riteria. The performan e of the proto ol is measured in terms of the average hannel utilization and the average waiting time. The waiting time is the time a message waits before it gets a reservation. We ondu t simulation experiments to study and ompare s heduling poli ies whi h are spe i ally designed to take are of the variable bit rate requirements of the users. The rest of the paper is organized as follows. Se tion 2 des ribes the working of the proto ol. In Se tion 3, we derive the analyti al model. Se tion 4 presents the s heduling algorithms while Se tion 5 summarizes the experimental results. Se tion 6 shows the possibility of further enhan ements and on lusions are drawn in the last se tion. FRAME

R T S

Data Slot 1

Data Slot 2

. . . . . . . . . . . . . .

Data Slot S

User U

No. of Simultaneous Users

1

User 1 User 2 User 3

2

C T S

3

S

1 2

U

No. of data slots

Figure 1: Frame stru ture of TDMA/CDMA proto ol 2. Proposed Proto ol

The two most important aspe ts of the proposed request-TDMA/CDMA MAC proto ol is the design of the frame stru ture and the s heduler at the base station as des ribed below. 2.1.

The Frame Stru ture

In our proto ol, time is divided into xed size frames whi h repeats itself, i.e, a new frame begins as soon as the previous one ends. A frame is divided into two

52


kinds of slots, the data slots and the ontrol slots. Control slots are further divided into request to send (RTS) and lear to send (CTS) slots as shown in Figure 1. Data Slot 1

Data Slot 2

Data Slot S

Code 1

Code 1

Code 1

Code 2

Code 2

Code 2

Code 3

Code 3

Code 3

Code U−1

Code U−1

Code U−1

Code U

Code U

Code U

Figure 2: Code allo ation for the data slots Ea h frame has S data slots of equal length whi h are used for transmission of data pa kets from the users to the base station (via uplink). It is assumed that one data slot an transmit one pa ket at a time. The RTS slots are used by the users to send their requests to the base station. The pro essing of requests and the s heduling are done during the CTS slots. A CTS slot is divided into S mini slots, ea h holding information of the orresponding data slot for the next frame. Ea h mini slot is further divided into U grids, where U is the maximum number of users who an transmit data simultaneously within a data slot. Ea h of these U grids is initialized with a CDMA ode (see Figure 2) that the s heduler allo ates to the user who su

eeds in getting a reservation for that slot. In a TDMA system, ea h data slot an be ex lusively used by one user at any point of time, whereas a CDMA system allows multiple users to share the same

hannel bandwidth at the same time. This is a hieved by assigning unique odes to all the users. The odes have the property that the ross- orrelation among any two odes is very low. We exploit this orthogonality property 15;2 to a

ommodate multiple users in one data slot. The maximum number of users who are allowed to transmit their data in one slot is restri ted to U as shown in Figure 2. Ea h user is allo ated a ode by the CTS. The ode is used to transmit data in one or more data slots in a frame. The number of data slots allo ated per frame depends on the bit rate requirement of the all. The data slots an be of two types { reserved and

ompetitive. The reserved slots are meant for a parti ular lass of traÆ and annot be a

essed by another lass, whereas the ompetitive slots an be a

essed by any

lass of traÆ . The number of reserved slots is not xed and varies from zero to a maximum, although the sum of the reserved and ompetitive slots is onstant. A user who su

eeds in reserving slots will have the reservation till the entire message is transmitted, irrespe tive of the number of frames required.


2.2.

53

The S heduler

The s heduler at the base station s ans the request queue that has all the in oming requests for all establishment along with all the other events o

urring in the system. The requests ontaining the bit rate requirements and the message lengths are maintained in the request queue in the sequen e in whi h they are generated. The s heduler allo ates data slots depending on the bit rate requirement. Higher bit rate alls are assigned multiple data slots in a frame, thus enabling the users to transmit more data per frame. The lowest bit rate request is treated as a single request and higher bit rates as multiples of the lowest bit rate. For example, if the requested bit rate is twi e the lowest bit rate then it is onsidered as two requests and hen e two data slots per frame are allo ated. Before pro essing the requests, the lass of the data traÆ is he ked and a de ision is made depending on the availability of reserved and ompetitive slots. 3. Performan e Analysis

For the sake of simpli ity, we make ertain assumptions for the system under

onsideration. We fo us only on the uplink traÆ , the ones from the nodes (hereafter nodes and users will be used inter hangeably) to the base station. Let us assume that the number of a tive nodes in the system is N. The duration of a frame is T se onds and the number of data slots per frame is S. Therefore, the time of ea h data slot is (T C R)=S se onds, where C and R are respe tively the duration of the CTS and RTS slots. We also assume the following. A1. Ea h node generates messages with a rate per frame, whi h is Poisson distributed. Also, whenever a message is generated, the entire message for whi h the onne tion is requested is ready. So we an say that the messages arrive in whole with a rate per frame. A2. In spite of assumption (A1), the nodes annot generate a new message until all pa kets of the urrent message are transmitted ompletely. Moreover, if a node ends transmission in the urrent frame, it does not generate a new message in the same frame. A3. Ea h message onsists of a number of pa kets, and the message length (measured in number of pa kets) follows a negative exponential distribution. The mean message length is Lm . A4. A node whi h has generated a message in the urrent frame annot a

ess the data slots in the same frame. It has to wait at least for the beginning of the next frame. A5. A node having a message to transmit and yet to establish a onne tion, stays in the queue and ontends for the data slots in every su

essive frames till it

54


gets a reservation. It might be removed from queue if the waiting message times out resulting in the all being dropped. A6. The number of data slots that an be allo ated to a node will depend on the bit rate requirement of the node. The number of data slots allo ated per frame remains xed for the entire length of a message. A7. A node after getting a reservation goes into the transmission phase and ontinues to transmit the entire length of the message. No reserved slots goes empty as a onsequen e of assumption (A1). We onsider m types of traÆ having bit rate requirements in the ratio of 1 : 2 : : m. Let the number of data slots required by a node per frame be b, whi h

an take values between 1 and m depending on the bit rate requirement. In other words, when a node is allo ated data slots, it will be allo ated a minimum of 1 and a maximum of m slots per frame so as to omply with the minimum requirements. As dis ussed earlier, the CTS slot has S olumns and U rows. So, there are S U (refer Figure 2) slots in a frame ea h of whi h an transmit a pa ket. Ea h of these DS = S U data slots are either reserved or unreserved. Let p be the probability that a data slot is unreserved and (1 p) be the probability that it is reserved. Ea h of the N nodes in the system an be in one of the three possible states; (i) thinking state, i.e., the node is yet to generate a message, and so has not entered the request queue; (ii) ontention state, i.e., the node has generated a message and is in the request queue ontending to get a reservation; and (iii) reserved state, i.e., the node has obtained a reservation for the entire message and is under transmission. 3.1.

Markov Model

The number of nodes in ea h of the three states are given below. N : Number of nodes in ontention mode Nr : Number of nodes in reserved mode Nt : Number of nodes in thinking mode The state of the system with (N + Nr + Nt ) = N nodes will not be ompletely determined by only one variable be ause for the same number of nodes in the system, there an be various ombinations of the number of nodes waiting in the queue and in the reserved state. As the number of nodes in the system is xed to N, we an

ompletely des ribe the state of the system with a tuple having two omponents. We model our system as a two-dimensional Markov hain in whi h a state an be

ompletely represented by the tuple (N ; Nr ). The performan e of the system an be evaluated by studying the distribution of the state variables. The system is fully known at the end of the CTS, i.e., at the end of ea h frame. So, we an take this point as the embedded Markov point. The state of the system that is rea hed at the end of ea h frame depends only on the arrivals, the departures and the result of the ontention pro ess during the interval of that


55

frame only. Hen e, the frame boundary is an ideal pla e to represent the system evolution, as a Markov hain. Let us assume that the state of the system after the nth frame be represented by (n ; nr ), and after the (n + 1)th frame by (l ; lr ).

nc

nr

lc

lr

State after (n+1)th frame

State after nth frame

Figure 3: Transition of one state to another Let A(n) be the number of requests for reservation, D(n) be the number of nodes departing after transmitting their message, and S (n) be the number of nodes that are su

essful in getting a reservation during the interval between nth frame and (n + 1)th frame. So, we have, l = n + A(n)

S (n)

(3.1)

lr = nr D(n) + S (n) (3.2) Given N, the system has a nite number of states whi h an be given by the tuple (N ; Nr ). Let Nr = nr , Nt = nt and N = n be the number of nodes in the reserved, thinking and ontention states respe tively. So, we an write the following

onstraints 0 nr Y = min(Ds ; N) 0 n N 0 nt N where DS = S U is the number of data slots. 3.2.

Cardinality of the State Spa e

The ardinality of the state spa e is nothing but all possible ombinations of the tuple (Nr ; N ) with the onstraint that nr +n +nt = N. Therefore for a xed value of n , nr varying between 0 and Y, the possible number of states that (n ; nr ) an take is given by Y X

(N

nr =0

nr + 1):

(3.3)

So the ardinality of the state spa e is Y )(Y + 1) 2 As Y is upper bounded by N, the state spa e size is O(N 2 ). (N + 1

(3.4)

56


3.3.

Transition Probabilities

In a Markov hain 11 , if the system is in state i, then there is a xed probability Pij that it will next be in state j regardless of the pro ess history prior to arriving at i. We refer to Pij as the transition probabilities, whi h satisfy Pij 0 and P1 j =0 Pij = 1 where i = 0; 1; ::: Thinking Mode

nt

Contention Mode

A

nc

Reserved Mode

S

nr

D

Figure 4: The transition probabilities To al ulate the elements of the state transition matrix, we need to al ulate the transition probabilities P rf(n ; nr ) ! (l ; lr )g. The transition between the dierent modes is as shown in Figure 4. 3.3.1. Probability of New Arrivals (A) We have assumed that the arrival rate of messages is per node per frame. Given that the number of nodes in the thinking mode is nt and the frame length is T , the probability that there are j arrivals, is given by the binomial distribution !

A(nt; j; ; T ) = njt e

T (nt j ) (1

e

T )j

(3.5)

3.3.2. Probability of Obtaining Reservation (S ) In ea h frame there are DS slots whi h an either be in a reserved state or in an unreserved state. Let p be the probability that a slot is in an unreserved state. Consider a request whi h has a requirement of b slots per frame. A single ode has to be assigned to the b slots, whi h ee tively means that the b slots should be from the same row (see Figure 2). For the request to get a reservation, there must be at least b unreserved slots in the same row. Therefore, the probability of a node in the

ontention state going to the reserved state, is equal to the probability that there is at least one row with at least b unreserved slots. The omplement of this is to nd the probability that all the rows have stri tly less than b unreserved slots, whi h is given by p(n1unreserved < b) p(nUunreserved < b) (3.6)

where p(niunreserved < b) is the probability that the number of unreserved slots in the ith row is less than b. As the status of ea h row is independent of that of the other, the above expression redu es to [p(nunreserved < b)℄U . The probability of having i unreserved slots out of S slots is given by Si pi (1 p)S i . The probability that a


57

node does not get a reservation in any of the U rows is obtained by summing the probabilities of having 0 to b 1 unreserved slots whi h is b 1 X

i=0

!

S i p (1 i

p)S i

U

(3.7)

The probability, q, that a request with requirement of b data slots gets a reservation is then given by ! U b 1 X S i S i (3.8) p (1 p) q=1 i=0 i Thus, for j nodes to go from the ontention mode to the reserved mode, given that there are n nodes in the ontention mode, is given by !

S (n ; j; q) = nj qj (1

q)n

j

(3.9)

3.3.3. Probability of Departures (D) To nd the probability that there are j departures, given that there are nr nodes in the reserved mode, we should take into onsideration the probability of departures of all lasses of traÆ separately. Let us assume that there are ji departures from ni nodes in the reserved mode where P ni is the number of nodes belonging to lass i, for i = 1; 2; ; m. So we have nr = m i=1 ni . For a node in transmission mode belonging to lass i, the probability of departure is Lim , where Lm is the mean message length. If the base station an keep a ount of the number messages in ea h lass undergoing transmission, then the probability that there are ji departures from ni nodes in the reserved mode is given by !

n i P r[jidep ℄ = i ( )ji (1 ji Lm

i ni ) Lm

ji

(3.10)

Therefore, the probability of a total of j departures from all the lasses ombined is given by X P r[jdep ℄ = P r[j1dep ℄ P r[jmdep ℄ (3.11) j1 jm P with the onstraint that j = m i=1 ji . We denote the probability of j departures from nr nodes in the reserved mode as

D(nr ; j; Lm) = P r[jdep℄:

(3.12)

3.3.4. Combined Probabilities We will now onsider all the possible ways in whi h the state (n ; nr ) an go to the state (l ; lr ) with all the onstraints satis ed. Let us say, l n = k and

58


lr nr = l where k and l an be either positive or negative. Depending upon the values of k and l, four ases may arise for P rf(n ; nr ) ! (l ; lr )g.

Case (i) k 0; l 0 P P rf(n ; nr ) ! (n +k; nr +l)g = Zj=l A(nt ; k+j; ; T )D(nr ; j l; Lm )S (n ; j; q) where Z = min(n ; nt k; nr + l)

Case (ii) k 0; l < 0 P P rf(n ; nr ) ! (n +k; nr l)g = Zj=0 A(nt ; k+j; ; T )D(nr ; j+l; Lm )S (n ; j; q) where Z = min(n ; nt k; nr l)

Case (iii) k < 0; l 0 P P rf(n ; nr ) ! (n k; nr +l)g = Zj=X A(nt ; j k; ; T )D(nr ; j l; Lm )S (n ; j; q) where X = max(k; l) and Z = min(n ; nt + k; nr + l)

Case (iv) k < 0; l < 0 P P rf(n ; nr ) ! (n k; nr l)g = Zj=k A(nt ; j k; ; T )D(nr ; j+l; Lm )S (n ; j; q) where Z = min(n ; nt + k; nr + l)

3.4.

Expe ted Waiting Time

The expe ted waiting time of a request in the ontention mode will be given by (expe ted number of frames) TP, where T is the duration of a time-frame. Also, (expe ted number of frames) = 1 i=0 ipi where pi is the probability that it waits for i frames. We regard the probability of a request leaving the queue after waiting for one frame as p1 and think of it as the probability of su

ess in Bernoulli trials. Note that the probability of waiting for the se ond frame is independent of the fa t that it waited for the rst frame, therefore we an regard the various frames as separate but similar experiments in the spirit of Bernoulli trials. A known result in Bernoulli trials states that the expe ted number of experiments to be performed before su

ess is rea hed is p11 . Therefore, it follows that the number of frames a request waits before leaving the queue is given by p11 . 3.4.1. Corre tion Term The above analysis assumes that arrivals would o

ur only at the beginning of a frame. This might not exa tly be the ase be ause arrivals ould o

ur at anytime within that time frame. Here we note that departures from the queue however


59

o

urs only at the end of a frame. To make the orre tion term for the arrival time within a frame, we assume as earlier that the probability of arrival in a frame is equally distributed over the time period of the frame. Thus, the expe ted time of arrival in that frame is T2 . In other words, the waiting time in the rst frame whi h we assumed to be T , is a tually T2 . So the orre t expe ted waiting time is E(w) =

1 p1

T+

T 1 = 2 p1

T 2

(3.13)

Let us now al ulate p1 . Re all that p1 is nothing but the probability that a request does not get a reservation and waits for a time equal to the frame length. This probability has already been al ulated as p1 =

b 1 X

i=0

!

S i p (1 i

p)S

i

U

(3.14)

Hen e the expe ted waiting time is given by E(w) =

1 Pb

1 i=0

S pi (1 i

p)S i

U

T 2

(3.15)

4. Proposed S heduling Algorithms

The s heduler at the base station s ans through the request queue and tries to allo ate slots as requested by the nodes. A node an only transmit if it gets a reservation for the data slots. If the s heduler nds enough empty slots to a

ommodate a new request with its bit rate requirement, it reserves slots for the entire length of the message. The non-servi ed request are again onsidered for the next frame and this pro ess ontinues till the request gets a reservation or is for efully dropped from the queue. Ea h CTS grid has a ounter whi h keeps tra k of the number of pa kets remaining to be transmitted, so that it an maintain the reservation till the end of the transmission. At the end of a transmission, the ounter is set to 0 whi h implies that the ode has been released and it an be assigned to the next possible node, if any. On e a reservation is made, the node has to transmit pa kets and no free slots will be allowed. This is due to the assumption of bulk arrival of the entire message. We rst present two simple s hemes and study their performan e with respe t to average waiting time and hannel utilization. Then we propose a third s heme as a hybrid of the rst two s hemes. These three s hemes mainly deal with how reservation is done for various lasses of traÆ . For brevity, we onsider four lasses of traÆ . The ratios of their bit rate requirements are 1:2:3:4, whi h means that the requests in ea h lass require 1, 2, 3 or 4 data slots per frame, respe tively.

60


4.1.

S heme 1 : No Reservation

Sin e none of the slots is reserved for any parti ular lass of traÆ , any node requesting for data slots an ontend for any unreserved slot. The s heduler at the base station observes that if a node is allo ated multiple data slots in a frame, the same ode is used, i.e, the data slots must belong to the same row. 4.2.

S heme 2 : Complete Reservation

In this reservation s heme, data slots are identi ed for ea h lass of traÆ and only the intended lass an use the orresponding reserved data slots. The maximum number of data slots a parti ular traÆ an have depends on the arrival rate of that

lass of traÆ . We assume that the requests from all the lasses are equally probable. The reservation made for the four lasses onsidered is as shown in Figure 5. It an be seen that the ratios of reservation for the four lasses also follow 1:2:3:4. First, the s heduler he ks the bit rate requirement (say b) of the request. Then it tries to allo ate slots from those already reserved for that parti ular lass. If it nds so, then it reserves b slots for the next d Lb e frames, where L is the length of the message. The request will not be allo ated slots if all data slots meant for that lass are already reserved, even if data slots for other lasses are available. Data Slot 1

Data Slot 2

Data Slot 3

Data Slot 4

Data Slot 5

Code 1

Resv. for Class 1 Resv. for Class 4 Resv. for Class 4 Resv. for Class 4 Resv. for Class 4

Code 2


Code 3


Code 4


Code 5


Code 6


Code U-1 Resv. for Class 1 Resv. for Class 4 Resv. for Class 4 Resv. for Class 4 Resv. for Class 4 Code U


Figure 5: Reservation for various types 4.3.

S heme 3 : Partial Reservation

The previous two s hemes have ertain drawba ks with respe t to ertain lasses of traÆ when working independently. To eliminate those limitations, we derive a hybrid s heme in whi h not all the data slots are reserved, nor are they left


61

unreserved. Instead, some data slots are reserved for ea h lass of traÆ depending on their relative arrival rates and some data slots are not reserved for any lass. The unreserved slots an be assigned to any lass of traÆ whi h does not nd slots from the reserved slots for that lass. On the arrival of a request, the s heduler rst tries to allo ate slots whi h have been reserved for that lass. If it annot be a

ommodated, then the s heduler look for unreserved slots from the ommon pool. 5. Simulation Results

The system onsidered in our simulation experiments onsists of only one ell in whi h there are N = 64 a tive nodes (or users) whi h are generating messages to be transmitted to another node. The rate of generation of messages is Poisson distributed with a mean of messages per node per frame. Ea h message has a

ertain length whi h is exponentially distributed with the mean size of Lm = 50 pa kets. This also means that on an average ea h message will require 50 data slots for its transmission. We use frame-time as the unit of time. We have onsidered ve data slots in a frame whi h o

upy 90% of the frame duration and the two ontrol slots (RTS and CTS) o

upy the remaining 10% of the frame duration. One data slot time is the time taken for the transmission of one data pa ket. Maximal Length 9

odes of length 15 were used and there were 15 su h odes whi h were allo ated to every data slot. Therefore, at any time a maximum of 15 nodes an transmit data simultaneously. We onsider the average waiting time and hannel utilization as the performan e measures. For hannel utilization, we do not onsider the ontrol slots and only onsider the utilization of the data slots. The performan e of S heme 1 is shown in Figure [6℄. It is observed that the traÆ with higher bit rate requirement were delayed more than the traÆ with lower bit rate requirement. This is due to the fa t that it is less probable to a

ommodate requests with larger bit rate sin e the same ode has to be used for all the data slots. The performan e of S heme 2 is depi ted in Figure [7℄ where traÆ of lass 1 had a onsiderable amount of delay. This is due to the assumption that the mean message lengths of all the types are same and lass 1 required more time to va ate the reserved slots sin e it ould only transmit one pa ket per frame, whereas the other types transmitted more number of pa kets in a frame and va ated the reserved slots after the transmission was omplete. So, for the same mean message length, the nodes with higher bit rates needed less time for the transmission. As all the 64 nodes randomly generated traÆ belonging to all four lasses, more lass 1 traÆ got queued due to its low probability of departure, resulting in very high waiting time. For S heme 3, a total of 8 odes (rows) were reserved for the various traÆ types. The ratio of reservation of ea h lass was based on the average requirement for that lass. The remaining 7 odes were left unreserved and any lass ould a

ess it. The hannel utilizations of the three s hemes are ompared in Figure 9. Though the hybrid S heme 3 has the same waiting time as S heme 1, it performs better in


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Figure 9: Average hannel utilization for the three s hemes terms of hannel utilization. In fa t the hannel utilization of S heme 3 is very lose to 100%, whi h means that there were very few data slots whi h were not allo ated to any node and thus were wasted. The reserved slots atered the minimum steady

ow, whereas the unreserved slots were used for the u tuations in the arrivals of the requests of dierent lasses. 10

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Figure 10: Performan e of Class 1 and 2 To validate the orre tness of the analyti al model, we ompare it with simulation results. The omparisons shown in Figures 10-11 is for S heme 1. For all the four

lasses onsidered, we obtain the average waiting time for dierent values of hannel utilization. We observe that the waiting time for lasses 1 and 2 are appre iably low even when the system is loaded. But for lasses 3 and 4, the waiting time blows up when the hannel utilizations are 0.8 and 0.7 respe tively. 6. Enhan ement of the Hybrid S heme

The hybrid s heme dis ussed above assumes that jobs an wait in the ontention

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Figure 11: Performan e of Class 3 and 4 mode inde nitely. However, in reality, a user might not want to wait inde nitely and would like to try again. Waiting inde nitely not only in reases the average waiting time but also is highly undesirable. There is generally a timer fun tion that de ides the maximum waiting time for a job in the queue. On the expiration of the timer, the all is removed from the queue resulting in all blo king. Also, there is a possibility of using su h odes whi h allow more users into the system. In that ase, the odes will not provide zero ross- orrelation and there would be some mutual interferen e among the odes whi h would introdu e some error at the de oder side. 6.1.

Introdu tion of Blo king

The performan e of the proposed proto ol with respe t to the average waiting time an be enhan ed by introdu ing an expiration timer. If a job is not allo ated slots within a pre-de ned maximum waiting time, then the all is blo ked. Thus, maximum waiting time for a parti ular traÆ lass sets an upper bound on the average waiting time. The ratio of the number of alls blo ked to the total number of alls generated gives the blo king probability of the system. To investigate the relationship between the maximum waiting time and the blo king probability, we initiated the expiration timer with a pre-de ned value for ea h of the traÆ lasses. The maximum waiting time for lass 1, lass 2, lass 3 and lass 4 were 5, 15, 20 and 30 frames respe tively. With these parameters, all others remaining the same, we have found the the blo king probability for dierent values of . We observe from Figure 12 the de rease in the average waiting time and the orresponding blo king probability. 6.2.

Use of Gold Codes

For our simulation purposes, so far we have used Maximal Length (ML) odes. These ML odes did not give rise to any error after de oding the spreaded signal at

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Figure 12: Average waiting time and blo king probability with expiration timer the re eiver. In the ase of ML odes, for a ertain length L of the ode, there exists exa tly L su h odes. The ML odes have the disadvantage that their number is limited. This is one of the main reasons to look for non-ML odes that do have a

ertain degree of orthogonality. In other words, if we look for some other types of

ode for whi h the number of odes available for a ertain length of ode is more, then more number of users an be a

ommodated simultaneously. This means that more number of bits an be suitably oded and transmitted. Gold Codes 12 are su h kind of odes whi h are obtained from ML odes. For a ode length of L, there are L+2 odes. But the usage of Gold Codes introdu es some error be ause these odes are not perfe tly orthogonal to ea h other. Gold Codes will in rease the hannel utilization, in a sense it will allow more information to be sent in the same data slot, at the ost of some error. Gold odes annot be used for appli ations whi h

annot tolerate any error but it an be used for voi e ommuni ation, say, whi h

an tolerate some errors. To see the ee tiveness of Gold odes, we simulated a system onsisting of 64 nodes. The rate of arrival of messages per node was varied from 0:01 to 0:1 per frame and the mean message length was taken to be 20. Gold Codes used were of length 15. The number of su h odes obtained were 17. The parameters were so

hosen as to bring out the dieren e in hannel utilization due to the use of Gold Codes. For the parameters dis ussed earlier, we observe from Figure 13 that the hannel utilization has in reased with the use of Gold Codes as ompared to ML odes by a fa tor of (L + 2)=L, with the introdu tion of some errors. The errors o

urred be ause the odes were not ompletely orthogonal. This kind of error is usually very small and an be tolerated for voi e ommuni ation. We also nd that the system performan e degrades with in reased load. Thus, we an say that if the system load is in reased, more error is introdu ed and all the nodes suer similar bit error rate.

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We have proposed a new MAC proto ol for supporting multimedia traÆ in wireless networks. The proto ol uses CDMA laid over TDMA and is hen e alled request-TDMA/CDMA proto ol. Data slots and ontrols slots make up the time frames. If a user wants to transmit a message then it makes a request to the s heduler whi h tries to allo ate data slots to the user. The s heduler takes into onsideration the time of generation of a all, the bit rate requirement and the message length while reserving slots for the entire length of the message generated. Three s heduling algorithms are proposed and their performan es are studied for four lasses of traÆ whi h have dierent bit rate requirements. We also model our proto ol using a two-dimensional Markov hain, and for a given system load we ompute the state transition probabilities and derive the average waiting time. By simulation experiments we show that our (hybrid) request-TDMA/CDMA proto ol is able to ee tively ombine the orthogonality of both time and ode division multiplexing. Further enhan ements are also proposed to de rease the waiting time and to in rease the average hannel utilization. 8. A knowledgements

The authors would like to thank the support of Texas Advan ed Resear h Program grant TARP-003594-013 and Texas Tele ommuni ations Engineering Consortium (TxTEC). Referen es

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