583

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-32, NO. 5 , MAY 1984

Message Delays fora TDMA Scheme Under a Nonpreemptive PriorityDiscipline LUIS F. M. DE MOMES, MEMBER,IEEE,

Abstract-A TDMA access-control scheme operating under a nonpreemptive message-basedpriority discipline is consideredand analyzed. The moment generating function (MGF) of the message waiting-time is obtained, at an arbitrarystation ofthe network, under the assumptions of a Poisson messagearrival stream and random message lengths governed by a general distribution, for each priority class. Using these results, explicit formulas forany moment ofthe message delay can be obtained. In particular, expressions for the average and standard deviation of the message waiting-time are presented, for the case when shod (e+, interactive) messages have priority over longer (e&,batch) messages.

I. INTRODUCTION E consider a multiple access communication channel which is intended to serve a population of N ( > 2 ) stati'ons, each wishing to transmititsdata messages across the channel. A satellite community of earth stations, a terrestrial radio channelproviding thecommunication medium toa number of data terminals, a localarea communications network,ora multiplexedlink inacomputernetwork serve as examples. The sharing of the channel by the network users (stations) is supervised and controlled by the underlying access-control discipline. Amultitude of access-controlschemes have been devised and studied. In particular, one can distinguish among procedures involving fixed-assignment schemes [ 1I , [ 21 , reservationschemes [ 21, [ 31, polling schemes [41, random access schemes [ 51 -[ 71 , or procedures which integrate several of the above-mentioned schemes [ 81, [ 91 . Fixed assignment schemes are easy to implement, manage, control, and utilize. These schemes have been used in several multiaccess communication channels. Under a fixed assignment scheme, each active station in the network is assigned a fixedchannel transmission timeand/orbandwidth slots. In particular, TDMA (time division multiple access) fixed assignment schemes are frequently used due to their flexibility and adaptability characteristics. Under a TDMA scheme each station is assigned, on a fixed basis, channeltransmissiontimes. Thus, time is divided into successive periods of constant duration called (time) frames. Each frame is subdivided into M(>N) successive slots. A slot is assumed to be T secondslong, We consider the general situation where station i can be assigned ni slots/frame (ni 2 1) which areuniformlydistributed (equally spaced) over the

Vv

Paper approved by the Editor for Computer Communications of the IEEE Communications Society for publication after presentation at Globecom '82, Miami, FL, November 1982. Manuscript receivedApril 15, 1982;revised June 15, 1983. This work was supported by the National Science Foundation under Grants NSF ENG 77-20799 and NSF ECS 80-12568, by the Air Force Office of Scientific Research under Grant AFOSR 820304, by the Office of Naval Research under Contract ONR-N00014-75-C-0690, by the Naval Research Laboratory under Contract NRL-N00014-78-C-0778,and by CAPES, Ministry of Education-Brazil, under Grant 24W/76. L. F. M. deMoraes is withtheInstitutoMilitardeEngenharia,Praia Vennelha, RJ 20.000 Brazil. 1:Rubin is withtheDepartment of Electrical Engineering, University of California, Los Angeles, CA 90024.

AND IZHAK

RUBIN, SENIORMEMBER,IEEE

frame. Thus, we assume that a different number ofslots can be allocated to different stations.Therefore,astation can be allocated a number of slots which is proportioud to its traffic. As forother access-controlschemes, theperformanceof sy'stems operating under a TDMA discipline can be measured in terms of its delay-throughput function. The latter describes the variation of message time delays (from the instant of their generation, or arrival at the station, to the instant of their successful reception by the destination station) as a function of the total information traffic carried by the communication channel. In terms of these indexes of performance, we note that fixed assignment access-controlschemes can provide an efficient way to share the channel when the dedicated channel resources (time and bandwidth) are well utilized by each station. This is, for example, the case when each station isgoverned by a steady traffic stream. The need for message-based priority functions in TDMA schemes is very frequently encountered. In many applications we multiplex (join) thetrafficstreams generated by several users (terminals) for a multitude of applications over the same bandwidth, in order to achieve higher channel utilization. For example, interactive-type traffic streams are often combined withtrafficstreams governed by other applications,such as file transfer/batch services. In such applications, each message subprocess requires its own message-delay (response-time) grade of service. For that purpose, a priority function is incorporated, for example, by assigning a higher priority to interactive messages, and a lower priority to the hatchmessages. In this paper we derive the message delay performance of TDMA access-control schemes operating under a nonpreemptive priority discipline. Thepriorityfunction.morporated here assigns priorities to messages based on their precedence level. Under the assumptions of Poisson message arrival streams, and random message lengths governed by a general distribution, for each priority class, we obtain the (steady-state) MGF of .the message waiting-time atanarbitrarystation of the network. Message delay analysis for TDMA schemes under preemptive and nonpreemptive disciplines was recently performed by Rubin [ l o ] . Inthatpaper, message arrivals were model.ed as a discrete-time batch process. Thus, message arrivals were recorded at the end of the underlying time slot. Messagesof the same priority class arriving within the same time-frame were ordered for service at random, while such messages arriving in different frames were served on a first-come first-served basis. In turn, in this paper we assume messages to arrive, and to be recorded as arriving, inaccordancewith a continuoustime Poisson process, so that messages of the same priority class are served ona first-come first-served basis, even for arrivals that occur in the same slot (or time-frame). For t.he latter model, formulas for the average limiting message delay were obtained by
0090-6778/84/0500-0583$01 .OO

0 1984 IEEE

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584

IEEE TRANSACTIONS COMMUNICATIONS, ON

VOL. COM-32, NO. 5 , MAY 1984

the message waiting-time. These resultsshould be of prime The distribution and characteristic functions of B , ( k ) are, importance in the design and analysis ,of such priority-based respectively, defined as TDMA schemes. The system model is presented in Section 11. In Section 111 the message waiting-time analysis is carried out. Numerical results are presented in Section IV, for a TDMA system which and employs a shortest-message-first priority service discipline. m

11. THE SYSTEMMODEL We consider a TDMA scheme with N input stations. Each station is assigned, on a dedicated basis, channel transmission time and transmission slots. Thus, time is divided into successive periods called (time) frames. Each frame is composed of M successive slots indexed from 1 to M . Time slots identified by the same index, in consecutive frames, form a TDMA circuit. Generated messages are assumed to be composed of fixed data units called packets. These packets are then transmitted during the stations’ access times. The transmission time of a packet is made equal to the duration of a time slot. We let the duration of a time frame be TF (seconds) and that of a time slot be T (seconds), so that TF = M T . Station i is assigned ni slots/frame (i = 1, 2, -, N ) in auniformly distributed fashion. For the purpose of analysis, we assume M to bea multiple of ni, each i = 1, 2, --,N . We later generalize for the case in which N/ni is not an integer. Hence, according to its traffic, station i is granted access to the channel, in a periodic fashion, every T F ~= MT/ni seconds (or every M/ni slots), i = 1, 2, -, N . At each of the N stations, each arriving message is assumed of K differentpriority classes. The to belong tooneout message association with a priority class may depend, for example, on its length distribution, identity of source/destination, and/or its type (data, control, etc.). Messages arriving at a station are stored in a buffer; then, following a nonpreemptive priority discipline, each station schedules thestored messages for transmission across the channel. When the channel becomes available to a station, the highest priority message (among all messages residing in thestationbuffer) is transmitted. Messages of the samepriority class are ordered for transmission on a first-come first-served basis. Messages in the transmission state cannot be preempted. Before deriving the results for the general case, we solve for the simpler situationin which ni = 1, i = 1, 2, .-, N and N = M ; so that each station is allocated a single slot/frame. The first slot in each time frame is dedicated for transmission of messages by the first station, the second slot is dedicated to the second station, and so on. As will be shown, after solving for thissimplercase, we readily obtainthe desired results under generalassumptions.Hence, forthetime being, we assume M stations, each of which can access the channel only once during each frame. Since differentstations areallocated disjoint timeslots, the statistical behavior of each station is independent of that of any other station. Hence, the analysis will be concentrated at only one of the M network stations, say, station 1. At each station (and, in particular, at station 1) the message arrival stream is characterized by a Poisson point process, so that hk (expressed in messages per second) is the average arrival rate of class-k messages. Each message is subdivided into elementary units called packets. A packet is assumed to contain p - l bits. Setting the transmission rate of the channel (bit rate) to be C bits per second (bits/s), we make 7 equal to ( P C ) - ~ . Thus, it takes exactly one slot to transmit a single packet. The number of packets contained in the nth arriving message of priority class k is denoted by B , ( k ) ( k = 1, 2, --,K).It is l} is a sequence of independent and assumed that { B , ( k ) ; n identically distributed (i.i.d.) random variables for each k = 1, 2, ..., K. The time taken to transmit the nthmessage belonging to class k is represented as a , ( k ) . Notice that { a , ( k ) ;n > 1) is also a sequence of i.i.d. random variables.

>

111. MESSAGE WAITING-TIME ANALYSIS For the underlying station we define:

W , ( k ) = waiting time of the nth class-k message arriving at the station t

0; k = 1, 2,

..., K

rk = 1, 2;-,

K

fm

Fig. 1 illustrates the behavior of the channel, assuming the existence of only class k messages. From this figure, we observe that, if all existing messages are of class k,thenthe behavior of the system is very close tothat of an M/G/1 queueing system with arrival rate hk and service times S , ( k ) , characterized by

The fundamental difference is that messages arriving to an empty system will have to wait, due to the frame synchronization mechanism, to the start timeof their dedicated slot in the next frame.Such messages could be delayed even further if messages of higher priority arrive during their wait time. To avoid this complication in the analysis, the system is induced to be always nonempty (busy) by the following artifice. Subsequently we invoke the use of standard results of priority queueing [ 121 to complete the analysis. We note that such an artifice has been previously utilized in [ 131 t o derive the packet waiting-time distribution in a slotted (Pierce) loop. First, assume thatanextrahypothetical lowest priority 1, is incorporated, such that it only handles class, class K isingle-packet messages; thus

Assume the arrival rate of this class of messages to be sufficiently high so that the station is never empty (idle). Then, in steady state, the buffer will always contain, at any time, at least a single class-(K + 1) message, and any message arriving at the system will find it busy, so that, following the nonpreemptive priority rule, any arriving message has to wait for the beginning of the next frame in order to start its transmission. Therefore,atthe beginning of thenextframe,the message to be transmitted is going to be the one with highest priority, which has arrived in the previous frame (if any has arrived). Notice that this will introduce the frame latency delay which appearsin the analyses ofTDMA schemes [ 11, [ 2 ] , [ l o ] , [ I l l , [141-[161. This simple artifice provides us with the required synchronization mechanism for the TDMA structure. With its incor-

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5 85

DE MORAES A N D RUBIN: M E S S A G E D E L A Y S FOR T D M A SCHEME

I

TF

IDLE SERVICE SLOT:

-

MT

MESSAGE LENGTHS IPACKETSI: glk) 1

I

1; elk). 2; glkl 2 3

1; glkl 4

J

Fig. 1. Illustration of class-k message behaviorat station 1. poration, Takacs'results [ 121 for message delays in a nonpreemptive,priority-based, continuous-time queueingsystem can be directly applied. Bk( and Laplace-Stieltjes transform Thedistribution B,*(s) of S , ( k ) are then given by

.) m

Bk(X) =P(LS,(~)
2 Pk,ju(X - / T p ) ; j= 1

x

0

k = 1, 2,

-, K

Theorem: Consider a TDMA scheme,where thestation under consideration (called station 1) is assigned one slot within each time frame and whose messages belong to K different priority levels. If the system operates under a nonpreemptive priority discipline and the parameters are defined as earlier in this section, then the Laplace-Stieltjes transform of message waiting-time for class-k messages (in steadystate) satisfies, for v k = ~ i k ,hi T F . E ( B ~ ( ~<) )1, q o 4 0 ,

where u( .)represents the unit-step function,and Bz(S) =

=x m

m

e c S *d B k ( x )

PkJe-'iTF = & , ( e - S T F )

W$(S)

= k$(S

+ I \ k - 1 [ 1 - G,*(s)]1

(2)

where C$(s) is the root with smallest absolute value in w of the equation

j= 1

since P ( s , ( ~ =)/ T F ) = P ( B , @ ) = i) = @ k , j ;each i = 1 , 2 , S , ( k ) , denoted by and k = 1, 2, ..*, K . The ith moment of b k , i , is given by m

bk,i

'}

= x!?{[S,(~)] =

Xi

dBk(X)

and

K

ca

i= 1 .

k

I

r

m

2 1, then no properlimiting distribution exists. The reader is referred to [ 121 for a discussion about the B K + ~ ( X=) u(x - T F ) ; x 2 0 solution to (3). See also [ 17, pp. 625-6281 where the solution to such a functional equation is analyzed. (Notice that (3), ( 5 ) , B Z + ~ (=~e)p s T F b ~ 1 ,i+ = ( T F ) ~ . and ( 6 ) converge for every set of Pi,, for Re (s) B 0; see [ 17, p. 625 1 .) With these definitions, we are able to apply Takacs' results To just compute the moments of the message waiting-time, for nonpreemptive priorities in continuous time [ 121 directly, rather than solving for the roots in (3), it is only necessary to to obtain the message waiting-time MGF. All we have to do is calculate the derivatives of Gz(s) at s = 0. This is readily to plug our parameters and transforms into the formulasgiven obtained through differentiation of both sides of (3), whenin [ 121. This is given by the next theorem (cf. [ 12, Theorems ever this derivative exists. The first and second moments of the waiting-time of class1,41). By ( l ) , we have

If

qk

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586

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-32, NO. 5 , MAY 1984

k (in steady state) are respectively given by

The first and second moments of the message waiting-time, in steady state, are given by

and

The delay of a message is defined as the total time spentby the message to get through the system. It is equal to the sum ofits waiting-time and service-time. Denoting by D,(k) the delay of the nth message of priority class k , we have D,(k) =

W,(k)

+~,(k)

(9)

where

w2

=

m ( B 3 ) ~ F 3+ ( I - ~ ) T F ~ 3(1 - P )

+ [ h!?(B2)TF2] + b?(Bz)( 1 2(1 - PI2

-

p)TF3 (1 5)

Using (1 1)and (14), the average message delay is given by =T

+ [B,(k) - 11

*

TF

(10)

is thetotaltime elapsed since the firstpacket of thenth message startsits transmission, untilthe last packet of this same message is completelytransmitted. Notice that should not be confused with S,(k), which was assumed to be the service time for the nth message in the M/G/1 queueing system, idealizedearlier,in order to obtainthedistribution of W,(k). Then, from (9) and (lo), the averade delay s k is given by D k = Wk,l

= Wk,l

TF ++ {E[Bnck)] - 1}TF

+

i‘

E[B,(k)]

MM

‘1

-__.

TF

1)

(1

with w k , 1 given by (7). As a particular case of the theorem, if K = 1, one obtains the message waiting-time MGF for a regular TDMA scheme, as given by the following corollary. Corollary 1: In a TDMA scheme in which the arrival stream of messages is characterizedbya Poisson distributionwith intensity h (messagesls) and the terminal under consideration (terminal1) is assigned oneslot withineach timeframe; if the message lengths have distribution {& = P(B, = k ) ; k = 1, 2, -*}, moments bk = E [ B n k ] , such that b = b l < O0, b2 < O0, b ) < 00 and if p = hTFb < 1, then the distribution of the message waiting time, in steady state,is given by W*(s) =

(1 - p )

*

(1 - e-sTF)

TF[ s - h

+ U*(S)]

with m

If p 2 1, then thereis no stationary distribution.

(12)

which is the same expression derived by Lam [ 1 11 , who used a rather different approach. Before proceeding, we make the following observations related to previous performance analyses of TDMA schemes. In [ 111, Lam analyzed a priority structure which was the same as in this paper. Regular (nonpriority) TDMA was also analyzed in [ 11] by utilizing previous results for M/G/1 queues, where messages initiating busy periods have a service-time distribution which differs from that of messages transmitted during an ongoingbusyperiod.Results thereincluded only thefirst moment for the message delay. The approaches used in [ 141[ 161 and [ 181 were based onanimbedded Markov chain (IMC) technique. In [ 141, Chu and Konheim analyzed a regular (nonpriority, a single slot per frame allocated toeach station) TDMA scheme, and obtained the first moment of the virtualwaiting-time experienced by an hypothetical message bringing rn (virtual) data units to the system [ 14, eq. ( 7 ) J . In [ 161, Hayes employed the IMC technique to get the MGF of the virtual waiting time experienced by a message bringing m packets t o the system [16, eqs. ( l ) , (17), (18), (23), (26)l. He also assumed a nonpriority scheme with a single slot per frame dedicated to each station. Aein and Kosovych [ 15J and Kosovych [ 181 have also utilized the method of IMC to study TDMA schemes without priority rules. The schemes analyzed by themincludedmore general assumptionsabouttheslot allocation. They derived upperandlowerboundsforthe expected virtual waiting-time experienced by a message for a TDMA schemewithcontiguousslot allocations, andexact results for TDMA with distributed allocations [ 18, eqs. (4), ( S ) , (S)] . The simple method employed in the present paper has not utilized any of the techniques above.However, the are derived results due to Takacs [ 121, employed in this paper, by incorporating the imbedded Markov chain approach. We now generalize our result to include the assumption of uniformly distributed allocations of slots per frame t o each station. Recall that in our general TDMA model, n, slots per

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587

DE MORAES AND R U B I N : MESSAGE DELAYS FOR TDMA SCHEME

frame are allocated to station m ( m = 1, 2 , -, N ) and each time frame contains M ( 2 N ) slots. N. Assume M/n, to be an integer for each m = 1, 2, (Later, we will drop this restriction.) Under these assumptions, our results derived previously in this paper can be used to yield the limiting MGF of waiting-time, for class-k messages at station m. Define all previous parameters in this paper as related to station m (e.g., hk is the arrival rate of class-k messages, at station m ) . Then, replacing TF with TF/n,, formulas (2)( 6 ) give the limiting MGF, and (7)-(I 1) yield the limiting moments,for waiting-time and deiay of class-k messages at station m. If K = 1 (no priorities), replacing TF with TF/nm in (1 2)(16) we obtain results for the limiting MGF and moments of waiting-time and delay, at station m, in a nonpriority TDMA scheme with uniformly distributed allocation of slots/frame to each station. This later scheme has been previously suggested and analyzed by Kosovych [ 181, who derived results for the average of virtual delay experienced by a message bringing m (virtual)packets to the station's buffer. The technique employed in [ 181 was based on the method of IMC and, therefore, rather different from the oneutilized by us. Now, if Mfrt, is not an integer, replacing TF in the previous calculationswith [ M / n , J T orwith TM/n,l.r, where 1x1 and [ x i are,respectively, the biggest integer not larger than x and the smallest integer not smaller than x, would yield upper and lower bounds on nloments of message waiting-time and delay. We notice that, since in practice M is large as compared with n,, these bounds will be very close to each other. Finally, we notice that if more than one slotis contiguously allocated to a station, our results cannot be applied. Our feeling, however, is that the case of uniformly distributed allocation shouldprovidea lowerboundforthe average message waiting time.Comparisonsbetweenthese two schemes have shown that this is the case [ 181 .

p=O.O

..e,

F

7

2

4

6

8

10

MkSSAGE LENGTH

p=O.Q

/ 2

K IL

v

IV. NUMER~CAL RESULTS As an example of a TDMA systemwith message-based priorities, consider a TDMA channel with the shortest-messagefirst (SMF) discipline at eachterminal: Messages arrive at the terminal (say, terminal 1) at the rateh messages/s (or ~ T F messages/frame). An arriving message belongs to class k with probability K- ; k = 1, 2, -*, K. A class-k message consists o f k packets. For this particular situation, we have

MESSAGE LENGTH

Fig. 3. Standarddeviation of waiting time versus message length for a TDMA schemeunder the SMF discipline; p = 7 10 = 5.5xT~.

implying that

message waiting-time, obtahed by using (7) and (8), are illustrated for the case when K = 10,. Notice that, in those figures, the traffic intensity of the system is defined as p = QK =: ~ T F ( K-I-1)/2. As observed from the figures presented, for a TDMA channel operating under the SMF discipline, not only high-priority messages (short messages) have a Smaller waiting-time than low-priority messages (long messages), butthey also experience finitely bounded waiting-time levels even when the trafThe equilibrium condition for the kth prioritylevel becomes fic intensity is close to 1. It is noticed that the message waiting-time increaseswith the message length, as expected. This feature is often desirable since, for many typical applications, a much smaller waitingtime level is prescribed forshort messages (e.g., interactive: in Figs. 2-5, the averages andstandard deviations of the data traffic) than for longmessages (e.g., batch data traffic).

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IEEE TRANSACTIONS ON COMMUNICATIONS,VOL. COM-32, NO. 5, MAY 1984

10

MESSAGE LENGTH =IO h

w

9

, 10

a U

Y

W

z

c

$ -

2

IO

t

$ W

0

U

a w >

1

U

-1

10

.2

.4 .6 TRAFFIC INTENSITY

I

1.o

.a (P

‘q10‘5.51T~t

Fig. 4. Average of waiting time versus traffic intensity for a TDMA scheme under a SMF discipline.

MESSAGE LENGTH=10

/

a P

z a c rn

r

lo’-0

.2

.4

.6

TRAFFIC INTENSITY

.e

I .o

( p = n l 0 = 5.51TF)

Fig. 5. Standard deviationof waiting timeversus traffic intensity for a TDMA scheme under the SMF discipline.

REFERENCES [1] I. Rubin, “Message delays in FDMA and TDMA communication channels,” IEEE Trans. Commun., vol. COM-27, pp.769-777, May 1979. [2] I. Rubin, “Access control disciplines for multi-access broadcast channels: Reservation and TDMA schemes,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 516-536, Sept. 1979. [3] I. Rubin and L. F. de Moraes, “Performance analysis for an adaptive polling access-control scheme employing a dynamic reservation protocol,” in Conf. Rec., Nut. Telecommun. Conf., New Orleans, LA, Dec. 1981. [4] I. Rubin and L.,F. de Moraes, “Polling schemes for local c0mmunic.ation networks,” in Conf. Rec., Int. Conf. Cornmun., Denver, CO, June 1981. [5] N. Abramson, “The ALOHA system-Another alternativefor computer communications,” in Proc. AFIPS Fall Joint Comput. Conf.,1970, VOI. 27, pp. 281-285. [6] I. Rubin, “Group random-access disciplines for multi-access broadcast channels,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 578-592, Sept. 1978.

[7] J. 1. Capetanakis, “Tree algorithmsforpacket broadcast channels,” IEEE Trans. Inform. Theory,vol. IT-25, pp. 505-515, Sept. 1979. [8] I. Rubin, “Integrated random-accesslreservation schemes for multi-access communication channels,” Univ. California, Los Angeles, Tech. Rep, UCLA-ENG-7752, July 1977. [9] -, “New hybrid access-control schemes for l o c a l distribution networks,” inConf. Rec., Int.Conf. Commun.,Denver, CO, June 1981. [lo] y , “Message delay analysis of priority-TDMA access-control schemes for multiple-access communications,”in Proc. Conf.Inform. Sei. Syst., PrincetonUniv., Princeton, NJ, Mar. 1982. [ I l l S. S. Lam, “Delay analysis of a time division multiple access (TDMA) channel,” IEEE Trans. Commun., vol.COM-25, pp. 1489-1494, Dec. 1977. [12] L. TakLs, “Priority queues,” Oper. Res., vel. 12, no. I , pp. 63-74, 1964. [13] J. D. Spragins, “Simple derivation of queueing formulas for loop systems,” IEEE Trans. Commun., vol. COM-25,pp. 446-448, Apr. 1977. [14] W.W.ChuandA.G.Konheim,“Ontheanalysisandmodelingofaclass of computer communication systems,” IEEE Trans. Commun., vol. COM-20, pp. 645-660, June 1972. [15] J. M. Aein and 0. S. Kosovych, “Sateliite capacity allocation,” Proc. IEEE, vol. 65, pp. 332-342, Mar. 1977. [16] J. F. Hayes, “Performance models ofan experimental computer network,” BellSyst. Tech. .I., vol. 53, pp. 225-259, Feb. 1974. [I71 J. W. Cohen, The Single Server Queue, rev. ed. Amsterdam,The Netherlands: North-Holland, 1982. [18] 0. S. Kosovych, “Fixed assignment access technique,” IEEE Trans. Commun., vol. COM-26, pp. 1370-1376, Sept. 1978.

*

Luis F. M. de Moraes (S’72-A’73-S’76-M’78) was bornin Rio deJaneiro, Brazil, on May 24, 1950. He received the Bachelor’sdegree in telecommunications engineering and theM.S. degree in electrical engineering from the Pontificia Universidade Catolica do E o de Janeiro (P.U.C./R.J.) in 1973 and 1976, respectively, and the Ph.D. degree from the University of California, Los Angeles, in 1981. From 1974 to1976, he worked with theCentro de Estudos em TelecomunicaCtks (CETUC), a telecommunications research institution at P.U.C./R.J. From 1976 to 1981 he was with the Department of System Science U.C.L.A., at on a fellowshipfrom CAPES, an agencyof the Brazilian Ministry of Education. During this period, he also was a Research Assistant at U.C.L.A. and performed research in the fields of communication theory, queueing theory, and computer communicationnetworks. From 1981to 1983he worked atINPE, the Brazilian Space Research Institute, SHo Paulo, as Head of the Computer Networks Division. He is currently a visitor in the Departmentof Electrical Engineering at U.C.L.A. His main research interests are in computer commuriications, local area networks, packet radio networks, satellite communications, and queueingtheory. Dr. de Moraes is a member of the Associationfor Computing Machinery and the Brazilian Societyfor Computing (SBC).

*

Izhak Rubin (S’69-M’71-SM’83)wasbornin Haifa, Israel, onMay 22, 1942.Hereceivedthe B.Sc. and M.Sc. degrees, in electrical engineering from the Technion-Israel Institute of Technology, Haifa, in 1964 and1968, respectively, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ, in 1970. From 1967to 1968 he was employedby the Israel Aircraft Industry, working in the area of electronics and control engineering. From 1968 to 1970he was an RCA Fellow and Research Assistant in the Department of Electrical Engineering at Princeton University. Since1970 he has been on the faculty of the School of Engineering and Applied Science, University ofCalifornia, Los Angeles, where he is currently a Professor in the Department of Electrical Engineering. As a consultant to industry, he has been involved in the design and analysis of many communications and telecommunications systems and networks. He serves also as the President of the IRI Corporation, a leading teamof telecommunications and computer network experts that provides consulting and study services to industrialorganizations. His current interests are in the areas of telecommunication andcomputer networks, satellite communications, radio networks, communication systems, information theory, queueing systems, and stochasticprocesses. Dr. Rubin isa member of Eta KappaNu. He served as the Co-Chairman of the 1981 IEEE International Symposium on Information Theory.

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Message Delays for a TDMA Scheme Under a ...

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Frequency Control Scheme for AC Systems Connected by a. Multi-Terminal ... Multi-terminal HVDC system. 3 .... α and β: integral and proportional control gain.

Impact of Delays on a Consensus-based Primary Frequency Control ...
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A Client/Server Message Oriented Middleware for ...
Device software drivers installation and configuration are performed on the server .... PC computer host sees base communication board as a virtual serial port.

Tri-Message: A Lightweight Time Synchronization Protocol for High ...
dealt with: clock offset and clock skew (clock drift speed). Clock skew is ... well over Internet paths with high latency and high variability and estimates both offset ...

Supplemental Appendix for “Sending a Message: The ...
Feb 29, 2012 - The presidential term dummy variables, election year dummy variable, and presidential approval variable are meant to address the potential ...

Google Message Encryption - SPAM in a Box
any additional software, hardware, or technical training. • Automatic ... Auditable protection of emails containing regulated or company proprietary information.

A Message From Mother Nature.pdf
... apps below to open or edit this item. A Message From Mother Nature.pdf. A Message From Mother Nature.pdf. Open. Extract. Open with. Sign In. Main menu.

Google Message Discovery - SPAM in a Box
compared to software or appliance based solutions. ... Always On, Always Current Message Security: Routing messages through Google's market-leading.

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A Night under the Stars
May 29, 2015 - Guest pass procedures will be available at the time of ticket sales. Please remember tickets are not refundable and are nontransferable.

A Night under the Stars
May 29, 2015 - 7:00pm-Midnight. River Stone Manor, Glenville, New York. Attendance Policy. We realize that school is in session on May 29 and, therefore, want to stress the importance of attending school for the duration of the day. There is a possib

Google Message Encryption - SPAM in a Box
dictate that your organization must secure electronic communications. Whether it is financial data ... document hosting and collaboration),. Google Page ... Edition (K-12 schools, colleges and universities) and Premier Edition (businesses of all size

A Robust Acknowledgement Scheme for Unreliable Flows - CiteSeerX
net and the emergence of sensing applications which do not require full reliability ... can benefit from selective retransmissions of some but not all lost packets, due to ... tion or fading in a wireless network, or loss of ack packets in asymmetric

A Fault Detection and Protection Scheme for Three ... - IEEE Xplore
Jan 9, 2012 - remedy for the system as faults occur and save the remaining com- ponents. ... by the proposed protection method through monitoring the flying.

A Quality of Service Routing Scheme for Packet ...
Abstract. Quality of Service (QoS) guarantees must be supported in a network that intends to carry real-time multimedia traffic effectively. A key problem in providing. QoS guarantees is routing which consists of finding a path in a network that sati

A MOTION VECTOR PREDICTION SCHEME FOR ...
Foreman MPEG-2. 42.5% 55.4% 79.1%. Proposed 78.5% 86.3% 93.7%. Stefan. MPEG-2. 33.5% 42.2% 59.7%. Proposed 61.5% 66.6% 75.4%. Table 2 shows experiment results of the full search al- gorithm, the transcoding algorithm using MPEG-2 MV and transcoding a

A Scheme for Attentional Video Compression
In this paper an improved, macroblock (MB) level, visual saliency algorithm ... of low level features pertaining to degree of dissimilarity between a region and.