Performance analysis of CSMA/CD with slotted multiple channel on radio LANs

Performance analysis of CSMA/CD with slotted multiple channel on radio LANs Wuyi Yue and Yutaka Matsumoto

Slotted multichannel non-persistent CSMA/CD (carrier sense multiple access with collision detection) radio LANs with a finite number of stations are considered. A multichannel packet radio network is based upon frequency domain design techniques which reallocate the system bandwidth. Markov chain analysis is used to exactly derive the moment generating functions (m.g.f.s) of the output process and interdeparture times. Channel utilization, delay performance and higher moments are then calculated in terms of the number of network stations, the number of network channels and the channel access rate. Calculated results show that the multichannel CSMA/CD not only preserves preferable features of the single channel CSMA/CD, but also has advantages such as extensibility of capacity, effectiveness, reliability, adaptability and serviceability over the single channel case. These results can then be used to evaluate the performance of interconnected networks, multi-hop multichannel networks or integrated networks of voice and data.

Keywords: CSMA/CD, performance, radio LANs

A packet radio network is a store-and-forward packet switching system employing radio channel(s). It consists of geographically dispersed terminals communicating with each other or with a central station over a single or multiple radio channels, which may be stationary or mobile (computers, mobile terminals, etc.).

The CSMA and CSMA/CD protocols have now been widely accepted in multiple access broadcast LANs. In CSMA/CD, collisions can be detected by letting stations monitor the channel to see if they agree with the packets being transmitted. When a collision is detected, the

Department of Applied Mathematics, Faculty of Science, Konan University, 8-9-10kamoto, Higashinada-ku, Kobe 658, Japan (Email: [email protected]) Paper received." 12 June 1992; revised paper received." 12 August 1992

detecting station will immediately abort its transmission and send a noisy pulse informing all the stations, which in turn will prevent others from transmitting. If no collision is detected in 2a, then this station is assured of a successful transmission, where a is the propagation delay between the two furthest stations. The CSMA/CD protocol is also one of the most widely used access protocols over different LAN topologies.

Several pe r fo rmance studies of CSMA and CSMA/CD systems can be found lm. There are three variations of the CSMA and CSMA/CD basic strategy:

1. Non-persistent C S M A : if the channel is idle, send; if the channel is busy, wait a random time and try again. Because of the simplicity and the good performance of the non-persistent protocol, its analysis has received wide attention.

2. p-persistent C S M A : this is used for slotted channels. If the channel is idle, send with probability p and defer until the next slot with probability 1 - p . This is repeated until the packet is successfully sent, or until another station is sensed to have begun transmitting, in which case wait a random time and try again.

3. 1-persistent C S M A : this is a special p-persistent case, in which p - - 1. A ready station senses the channel, and if the channel is idle, it transmits the packet. If the channel is busy, it waits until the channel becomes idle and then the station transmits the packet with probability 1.

Recently, some studies have appeared in the literature on the performance analysis of a number of access protocols implemented in multichannel radio commu- nication systems 5-1°. In these studies, the network performance was analysed for ALOHA, CSMA and

0140-3664193/010637-08 © 1993 Butterworth-Heinemann Ltd

computer communications volume 16 number 10 october 1993 637

CSMA/CD with slotted multiple channel: W Yue and Y Matsumoto

CSMA/CD protocols. The control procedure of a multichannel CSMA or CSMA/CD system is almost the same as that of a single channel CSMA or CSMA/ CD system, except that the multichannel CSMA or CSMA/CD system has an additional mechanism, channel selection. Ajmone Marsan and Roffinella 6 considered two ways to select one from a number of identical channels to transmit packets:

1. CSMA/CD-RC: a station with a ready packet randomly selects one of M available channels. That part icular channel is then accessed using the conventional CSMA/CD protocol, independent of activities on the other M - 1 channels before sensing it.

2. CSMA/CD-IC: a station with a ready packet first senses all M available channels. Then out of all the channels sensed idle, the station chooses one randomly and accesses it using the conventional CSMA/CD protocol.

They showed that the multichannel scheme improves the channel throughput rate by reducing the number of users who can make simultaneous demands on the same channel, in addition to its preferable characteristics such as easy expansion ability, easy implementation by frequency division multiplexing technology, high reliability and fault tolerance. Todd s presented an exact analysis of the throughput for slotted multichannel CSMA/CD systems. Some priority schemes have also been proposed and analysed for the multichannel CSMA/CD protocols 9' 10

However, in most of these studies, multichannel systems have been analysed to obtain average performance measures. The design and development of multichannel multi-hop systems, and interconnected network systems or integrated networks of voice and data, require not only such average performance measures as throughput or packet delay, but also higher moments of the packet interdeparture time and number of departures in parallel.

We have an interest in the traffic characteristics of the output process and interdeparture times in multichannel networks to evaluate of the performance of the interconnected networks, since the output process from the system constitutes a part of the input process to another interconnected, neighbouring network or another set of channels. Using the first and second moments of the packet interdeparture time, we can determine the parameters in the diffusion approxima- tion to the input process of interconnected systems. Furthermore, to evaluate the performance of commu- nication networks such as a multi-hop system and a digitized voice system, the analysis has to be extended to provide delay distributions. Until recently, studies on the probability distributions of the packet interdeparture time and packet delay have only been concerned with the single channel systems in a number of access

protocolsll 14. However, the performance analyses of multichannel systems are quite different from those of single channel systems.

In this paper, we study the performance analysis of the finite population, slotted non-persistent CSMA/CD multichannel. The analysis is based upon Markov chain techniques, and gives the moment generating functions (m.g.f.s) of the output process and packet interdeparture times. We can calculate their average and higher moments by differentiating these m.g.f.s to compare with those of the single channel case. These results are useful for analysing multi-hop networks and integrated networks of voice and data employing these random access protocols.

S Y S T E M M O D E L

There are N mutually independent stations which communicate over M broadcast channels. All channels are assumed to have the same bandwidth in Hz and the stations' access is synchronized to the start c f time slots of z seconds each. The time slots are defined as synchronous across all M channels and amongst all stations. Each station sends its packets one-by-one, thus it is not allowed to transmit the next packet before it has finished the previous one. Without loss of generality, we assume M < N.

In mobile packet radio systems, it is well known that the time varying channel suffers fading, shadowing ignition noise, co-channel interference and from the Doppler effect due to mobile stations. It is possible to introduce a CSMA/CD with a spread spectrum scheme or an F H / F S K CSMA/CD (Frequency Hopping/ Frequency Shift Keying) 15 in the presence of partial- band noise interference. However, it would significantly increase the complexity of the performance analysis, so numerical experiments would be intractable. For this reason, this paper employs a fixed normalized propagation delay, and assumes that packet retransmissions are only due to collisions. The slot size is assumed to be the end-to-end propagation delay. The transmission time of a packet is denoted by T. T is assumed to have a geometrical distribution with rate r/, and is considered to contain both packet service time and propagation delay for each transmitted packet. All stations are synchronized, and start their transmissions at the beginning of a slot. It is assumed that each station attempts to access a channel with probability 2 at the beginning of a slot, and then one of the free channels is selected with equal probability (the IC strategy). Owing to the decentralized nature of this protocol, simultaneous transmission on a single channel by two or more stations can occur. When this happens, it is assumed that the transmission of all such stations is unsuccessful, and a collision is said to have taken place. The time between the occurrence of a collision on a channel and recovery from the collision is called the collision detection time. The time required for

638 computer communications volume 16 number 10 october 1993


collision detection is assumed to be one slot. Let x(t) denote the number of successfully transmitting stations at the beginning of the t-th slot. Under the above assumptions, we see that the process {x(t), t = O, 1, . . .} has a Markovian property. In the following analysis, we take x(t) as the system state.

PERFORMANCE ANALYSIS

')/('+'-r-, ') ( 0 _ < m < m i n ( r , n ) , l < n < N , 1 < r < M ) ( 3 )

where (~) is defined as:

= (a-b)] 0 <b < a otherwise

Output process

Let II = {no, h i , . . . , / rN} denote the (N + 1) dimensional row vector of the stationary state probability distribution of x(t) as t ~ o¢. H can be calculated by solving the set of linear equations, H = HP, ~N= 0 nj = 1, where P is the matrix of one-slot transition probabilities Pij. To obtain transition probabilities P,j, let us define the following probabilities:

G{alb} =

Q{kli } =

P{m In, r} =

Pr{a stations access channels ]b stations are not transmitting}, Pr{k transmissions complete [ i successful transmissions are in progress}, Pr{m successful transmissions are initiated ]n accessing stations see r channels idle}.

They are given by:

G{a[b}= (ba)2"(1-- 2)b-a (1)

Q{kli} = (k)~lk(1- q) i-k (2)

Next, we briefly explain how to obtain P{mln, r}. The number of distinct ways in which n stations can access r available channels is given by (,+r~l). The number of ways in which m succesful transmissions out of r channels is given by (m)" To obtain the number of ways in which n stations accessing r channels can result in exactly m successful transmissions, the above combinations must be multiplied by the number of ways that the remaining n - m stations can unsuccessfully access the remaining r - m channels. We choose a particular channel, say u. Clearly, channel u must either be idle or it must contain a collision. Thus the total number of distinct ways of assigning the remaining n - m stations unsuccessfully to the other u channels is (rum) k(n-m-u-l]u 1 1. Summing over all possible values of u, we get:

min([a'~'],r-m)>O

u=l

For transition from i t o j in a slot to occur, the following events must be satisfied at the same time:

1. Among N - i non-transmitting stations, n stations access channels.

2. Among n accessing stations, j - i + k stations succeed in transmission.

3. Among j + k stations, k stations complete their transmissions.

Expressing these events mathematically, we obtain:

Po.(k) = lim Pr{x(t + 1) =j,k stations terminate t - + ~

successful transmissions Ix(t) = i}

N i

= Z G { n l U - i } P { / - i + k l n ' M - i } n=j-i+k

Q{k IJ + k} (4)

Pij = lira Pr{x(t + 1) =jlx(t) = i} I~OO

= Z Po(k) (O<i<N,O<_j<_N) (5) k=0

Let O*(z) denote the moment generating function (m.g.f.) of the number of successful packet departures at an arbitrary slot boundary. Then we get:

N N M-j O*(z) = Z ni Z Z PO (k)zk (6)

i=0 j=0 k=0

The throughput 0 (defined as the average number of packets successfully transmitted per slot) is obtained by differentiating O*(z) at z = 1 as follows:

N N M ~

0 = Z gi Z Z Po(k)k (7) i=0 j=0 k=0

The average channel utilization is given by S = O/M.

Interdeparture time distribution of type-k

In this subsection, we derive the packet interdeparture time distribution of type-k. We define the packet



interdeparture time of type-k as the time interval between two consecutive slot boundaries at which the number of successful depar tures is equal to k ( k = l , 2 , . . . , M ) . We denote by y(k) the packet interdeparture time of type-k. Consider slot n (d) such that x(n (d)) = i. On the condition that x(n (a)) = i, the time interval from the beginning of slot n (a) to the first slot boundary, where k packets depart successfully, is denoted by X (k), and its moment generating function is denoted by xlk)*(z) ( i = 0 , 1 , 2 , . . . , N ) . x l k ) * ( z ) i s derived from the following observation; if k packets depart successfully at the end of slot n (a), then X (k) = 1. If the number of successful departures in slot n (a) is not k and x(n (a) + 1 ) = j , then the distribution of the time interval until the next type-k-departure has a moment generating function given by zX~k)*(z). By summing all probabilities on the above events, we can obtain XlkY*(z) as follows:

Joint probability distribution of packet interdeparture time and number of channels successfully transmitted

In this subsection, we analyse the joint probability distribution of packet interdeparture time and the number of channels successfully transmitted. We define the packet interdeparture time as the time interval between two consecutive slot boundaries, at which at least one packet departs. Note that this is different from the definition in the previous subsection.

Let W represent a random variable of packet interdeparture time, and let C (C = 1 ,2 , . . . , M) represent the number of packet departures in parallel when the departure satisfying the above definition occurs.

We define the m.g.f, of the number of successful departures and x(n (a) + 1 ) = j , given x(n (a)) = i as follows:

oo min(i, M)

Xlk)*(z) Z P r { X ( k ) l l x ( n (a)) i}z' (s), : = = Pij (4) = Z Pij(k)~k (0 < i < N, 0 <_ j < N) /=1 k = l (12)

N

= E z { e o ( k ) + [ t , , j - (8) j=O

Let X(k)*(z) . . . . {x~k)*(z),X{l')*(z), , a N''(I') . . . . ~z)) denote the (N + 1) dimensional row vector of the conditional

(k), m.g.f. X i (z). Expressing equation (8) in matrix notation, X (k)*(z) is given by:

x(k)*(z) = z{I -- zIP - P(k)]}- lP(k)H (9)

where H is the column vector with (N + 1) elements, all of which equal one, and I is the ( N + 1)× ( N + 1) identity matrix. P(k) is the ( N + 1)× ( N + 1) matrix whose elements are Pij(k). P is the matrix of the transition probabilities P0. Let ~i(k) (i = O, I, 2 , . . . , N) denote the stationary state probability distribution of state i at the slot boundary with type-k departure. We can obtain:

~(k) = ~(k){I - [P - p(k) ]} - lp(k)

N

j(k) = 1 j=O

(lO)

where ~(k)= { ~ l o ( k ) , ~ l l ( k ) , . . . , ~ l N ( k ) } is the ( N + 1) dimensional row vector of the stationary state probability distribution. Finally, we get:

(30

y(k), (z) = Z z'Pr{ y(k) = l} l=1

=- k~(k)X(k)*(z) (1 1)

To obtain the m.g.f, of the joint probability distribution of packet interdeparture time and the number of departures, we also define the conditional transition probability:

P!~) = Pr{x(n (d) + 1) = j , at least one packet departs U in slot n (a) I x(n(d)) = i}

(s)* = Po (1)

C o n s i d e r t he c o n d i t i o n a l m . g . f . T*(z,~) (i = 0, 1 ,2 , . . . , N) of the joint probability distribution of the random variables W and C given x(n (d)) = i. T*(z, 4) has the following meaning. When the system state changes to j at the beginning of slot n (d) + 1, if at least one packet departs successfully at the end of slot n (d), then W = 1, and the joint m.g.f, of the transition in this slot and the number of successful channels in parallel is given by p~S),(~). On the other hand, if there is no successful departure at the end of slot n (d), the joint m.g.f, of the transition in this slot, and the time interval from the end of slot n (d) to the end of the slot in which at least one packet is successfully transmitted, and also the number of departures in parallel at the end of that, is given by z [ P i j - P~S)]T](z,~). Summing over all probabilities on j, T~(z ,~) is obtained by the following expression:

T; (z, 4) = Pr{ W = l and C = h /=1 h=l

] x(n (d)) = i}zl~ h N

(s), (s) , = z Y ' ~ A e , j (¢) + [*'ij - 6 j ]r~(z,¢)} j = 0

(13)


C S M A / C D wi th s lo t ted mu l t i p l e channe l : W Yue and Y Matsumoto

In the same way as in the previous subsection, let T*(z ,~)={T~(z ,~) ,T*l(Z,~) , . . . ,T*u(z ,~)} b e a n (N + l) dimensional column vector; then we have:

T*(z, ~) = z{I - z[P - P(S)]}-'P(S)*(~)n (14)

where P(~)* (¢) and p(s) are ( N + 1) × (N + 1) matrices whose elements are p~S).(~) and P~.~)(i = 0, 1 , . . . ,N ; j = 0, 1 , . . . , N), respectively. P and H are as defined in the previous subsection.

To obtain the unconditional m.g.f. T*(z, ~) of packet interdeparture time W and the number of successful departures in parallel C, we first need to give the stationary state probability distribution immediately a f t e r a t l e a s t o n e p a c k e t d e p a r t u r e . L e t q , = {q~0, qS1,...,~bN} be an ( N + 1) dimensional row vector representing the stationary state probability distribution. It is given by solving the following equations (note that P(~) = p(s). (1)):

¢ = ¢{I - [P - p(s)]}-lp(s), N

Z , j : l (15) j=O

From T*(z, ~) and ~, we can finally get T*(z, ~):

T*(z, ~) = ~T*(z, ~) (16)

Interdeparture time distribution at a station

Here we derive the m.g.f. D*(z) of the packet interdeparture time at each station. Let us call a station which we focus on a tagged station. Since all stations are homogeneous in terms of channel access rate and transmission time, we can choose any station as the tagged station.

Suppose that the tagged station has just completed its transmission at the end of slot n (t), and finds the system in x ( n (t) + 1) = i. Let Di and D*(z) denote the random variable and the m.g.f, for the time interval from the beginning of slot n (t) + 1 with x(n (t) + 1) = i to next departure at the tagged station, respectively. DT(z) is obtained according to the following observation:

N i N- i

+Z Z j=l k=max(O,i-j) n=j-i+k

G { n I N - i } P { j - i+ kin , M - i}

• O{k l J + k} N N J i kzD](z) (17)

Let pO) denote an (N + 1) dimensional column vector whose i-th element is given by:

N- i min(n,M-i) l

[p0/]i = ~--~ ~ G { n i N _ i } P { l l n , M _ i } N _ i n=l 1=1

(18)

and let p(2) denote an (N + 1) × (N + 1) matrix whose (i,j)th element is given by:

[P(2)]8 = i N - i

Z Z k=max(O,i-j) n=j-i+k

G{n I N - i }e{ j - i + kin, M - i}

.Q{kl j + k} N - j - k N - i

(19)

Writing D~(z) in vector form, we have:

oz {I - zp(2/} la(~/ (20) D * ( z ) - 1 - ( 1 - q ) z

where D*(z) = {D~'(z), D~(z) , . . . , D~v(Z)} are N dimensional column vectors.

Let c 9 be defined as the probability that the tagged station sees the system in s ta te j when it has just finished its transmission. By using rti, Ps(k) and 0 given previously, we obtain ~j as:

N M - j p ~ i = 0 ~ k = l zti ij(k)k (21)

~J= 0

Finally, we obtain:

1. If the tagged station succeeds in transmission in s l o t n ( t )+ l , t h e n D * ( z ) = ~ l ( 1 - q ) 1-1 , l z t : , 7 z / { 1 - (l -

2. If the tagged station does not access or fails to transmit in slot n (t) + 1 and the system state changes from i to j, then D 7 (z) : zD; (z).

Considering probabilities for each case, we get:

N- i min(n,M-i) , rlz

D,(Z) - l _ 8 - _ , ) z n=l 1=1

l G{n IN - i}P{lln, M - i} N - i

N

D*(z) = Z ~jD](z) (22) j=l

N U M E R I C A L R E S U L T S

In the previous section, equations for calculating the probability distribution functions of the output process, interdeparture times and number of departures in parallel for slotted non-persistent CSMA/CD-IC were given. Using these equations, we obtain their average performance measures. By Var[G] we denote the va r iance of the r a n d o m var iab le G, Var[G] =

c o m p u t e r c o m m u n i c a t i o n s v o l u m e 16 n u m b e r 10 o c t o b e r 1993 641


E[G 2] - {E[G]} 2, and by CG the coefficient of variation of the random variable G, Ca = ~ / E [ G ] . Using these relations, the coefficients of variation of the packet interdeparture times and the number of successful departures are also obtained.

We compare systems where the sum of the multiple channel bandwidth is equal to the bandwidth of a single channel network, i.e. all M channels are considered to have the same bandwidth v in Hz, v = V/M, where V is the total available bandwidth of the system. In dividing the entire available bandwidth of the system into homogeneous partitions, the time slot size z over a channel with bandwidth v is given by r = Mr0, where v0 is the time slot size in a channel with bandwidth V. Therefore, as the number of channels is changed, the bandwidth of each must also change to satisfy the fixed total bandwidth constraint. When comparing system performance with different values of M, we have considered the fact that slot sizes are different.

In numerical examples, we consider a system with N = 30, ~/= 0.1 and the propagation delay a = 0.1. Figure 1 shows the average channel utilization S versus 2N (total offered rate in the system) for M = 1,3,5 cases, respectively, to see how the various channel utilizations depend upon M. The utilization for M = 1 is higher than the utilization for M = 3 and M = 5 when 2N is low, while as 2N increases, the utilization for M = 5 is higher than that for M = 1 and M = 3.

Figure 2 shows the average interdeparture time at a station. We can obtain this by differentiating the moment generating function D*(z). The average inter-

departure time is small in case M = 1 when 2N is light, but it becomes very large as 2N increases. The average interdeparture times are kept smaller in the multichannel ca.ses because the transmission times of a packet for the multichannel cases are longer than those for the single channel case, so that their interdeparture times are larger than those for the single channel case as long as the traffic is light• However, as 2N increases, multichannel systems suffer fewer collisions than do single channel systems. Our results agree with the conclusion in Reference 6, i.e. the multichannel scheme can improve channel utilization by reducing the number of users who can make simultaneous access to the same channel•

The coefficients of variation curves of the type-k packet interdeparture time (where k = 3), the packet in terdepar ture t ime W, the number of successful departures and the packet interdeparture time at a station are shown in Figures 3-5, respectively• Figure 3 shows that with M the coefficient of variation of the packet interdeparture time of type-k (where k = 3) decreases as 2N increases from zero.

In Figure 4, the coefficient of variation of the packet interdeparture time W is plotted as a function of 2N. We can see that the coefficient of variation of the packet interdeparture time W begins to decrease from 1.0, reaches a minimum value, and is sustained at a value that depends upon M. This behaviour can be explained as follows. When 2N is small, the interdeparture time consists of a very long idle period and a packet

o• . ~ o

o

r~ o3

<>

c ~

,5

// M3/ M = I

o c;i I I I I J 1 0.05 0.i 0.2 0.4 0.8 1.6 3.2

AN

Figure 1 Average channel u t i l iza t ion v e r s u s AN. N = 30; a 0.1

I 6.4

t~

M=3

\ M=5

" I I I I 1 I 1

0.05 0.i 0.2 0.4 0.8 1.6 3.2 6.4

F i g u r e 2 a : 0 . 1

AN

Average in te rdepar tu re t ime at a s ta t ion v e r s u s 2N. N = 30;



~ o

>

o

°o.0s

M=3

M=I

M=5

[ I I 1 I I l 0.1 0 .2 0 .4 0 .8 1 .6 3 .2 6 .4

AN

Figure 3 Coefficient of variation of packet interdeparture time of type-k versus 2N (k = 3). N = 30; a = 0.1

eq

o~

eq

¢0

. cq

H

,-4

~h

> co

~ . 0 5

Figure 5

M=3

M=5

I I I l [ [ I

0 . 1 0 . 2 0 . 4 0 . 8 1 . 6 3 . 2 6 . 4

A N

Coefficient of variation of packet interdeparture time at a station versus ).N. N = 30; a = 0.1

~= M=I

/

5

. = 3

~ - /

.~ M=5

o I I I I I I I

0 . 0 5 0 . 1 0 . 2 0 . 4 0 . 8 1 . 6 3 . 2 6 . 4

AN

Figure 4 Coefficient of variation of packet interdeparture time W versus .iN. N = 30: a = 0.1

transmission time, where it should be noted that the coefficient of variation for the former period is 1.0.

F i g u r e 5 shows that for the single channel case, coefficients of variation of the packet interdeparture

time at a station fluctuates the most. This is because as 2N increases, packet collisions happen more easily in the single channel case than in multichannel cases.

C O N C L U S I O N

In this paper, we have given a detailed study of the finite population, slotted, non-persistent CSMA/CD multi- channels. We exactly derived the m.g.f.s of both the output process and interdeparture times. In numerical examples, we examined the effect of the channel number on the average and coefficients of variation of the type-k packet interdeparture time, the packet interdeparture time W, the number of successful departures, and the packet interdeparture time at a station. From numerical examples, we see that multichannel broadband radio networks have advantages over single channel broadband radio networks, such as higher channel utilization by distributing traffic load on multiple channels in addition to higher reliability and stability. These results are useful for analysing multi-hop multichannel networks, interconnected networks or integrated voice and data networks employing CSMA/CD.

R E F E R E N C E S

1 Kleinrock, L and Tobagi, F 'Packet switching in radio channels: Parts I and II', IEEE Trans. Commun., Vol 23 No 12 (1975) pp 1400-1433



2 Tobagi, F and Hunt, V 'Performance analysis of carrier sense multiple access with collision detection', Comput. Networks, Vol 4 (1980) pp 245-259

3 Tobagi, F and Kleinrock, L 'Packet switching in radio channels: Part IV - Stability considerations and dynamic control in carrier sense multiple access', IEEE Trans. Commun., Vol 25 No 10 (1977) pp 1103-1119

4 Coyle, E and Liu, B 'Finite population CSMA/CD networks', IEEE Trans. Commun., Vol 31 No 11 (1983) pp 1247-1251

5 Yung, W P Analysis of Multichannel ALOHA Systems, PhD thesis, University of California at Berkeley, CA (1978)

6 Ajmone Marsan, M and Roffinella, D 'Multichannel local area network protocols', 1EEE J. Selected Areas in Commun., Vol 1 No 1 (1983) pp 885-897

7 Okada, H, Nomura, Y and Nakanishi, Y 'Multi-channel CSMA/CD method in broadband-bus local area networks', Proc. GLOBECOM, Atlanta, GA (1984) pp 6424547

8 Todd, T D 'Throughput in slotted multichannel CSMA/CD systems', Proc. GLOBECOM, New Orleans, LA (1985) pp 276-280

9 Ko, C and Lye, K 'A new priority multichannel CSMA/CD protocol', Proc. ICC, Toronto, Canada (1986) pp 136-140

10 Okada, H and Ikebata, H 'Priority schemes of multichannel CSMA/CD for advanced multimedia networks', Proc. GLOBE- COM, Tokyo, Japan (1987) pp 1607-1611

11 Tobagi, F A 'Distributions of packet delay and interdeparture time in slotted ALOHA and carrier sense multiple access', J. ACM, Vol 29 No 4 (1982) pp 907-927

12 Takagi, H and Kleinrock, L 'Mean packet queueing delay in a buffered two-user CSMA/CD system', IEEE Trans. Commun., Vol 33 No 10 (1985) pp 1136-1139

13 Takagi, H and Murata, M 'Output processes of persistent CSMA and CSMA/CD systems', IBM JSI Research Report, TR87-0015 (1986)

14 Matsumoto, Y, Takahashi, Y and Hasegawa, T 'Probability distributions of interdeparture time and response time in multipacket CSMA/CD systems', IEEE Trans. Commun., Vol 38 No 1 (1990) pp 54-66

15 Sinha, R and Gupta, S C 'Carrier sense multiple access with collision detection for FH/FSK spread spectrum mobile packet radio networks', Proc. 34th Vehicular Technology Conf., Pittsburgh, PA (1984) pp 142-147

644 computer communicatiohs volume 16 number 10 october 1993

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Performance analysis of CSMA/CD with slotted multiple channel on radio LANs