PERFORMANCE EVALUATION OF A REQUEST-TDMA/CDMA
PROTOCOL FOR WIRELESS NETWORKS
MAINAKCHATTERJEEandSAJALK.DAS
CenterforResear hinWirelessMobilityandNetworking(CReWMaN)
Departmentof ComputerS ien eandEngineering
UniversityofTexasatArlington
Arlington,TX76019-0015
Re eivedFebruary5,2000
RevisedJanuary27,2001
This paper proposes a new medium a ess ontrol (MAC) proto ol, alled
Request-TDMA/CDMA, forsupporting multimedia traÆ inwireless networks. In this hybrid
proto ol,CDMA( odedivisionmultiplea ess)islaidoverTDMA(timedivision
multi-plea ess),whereatimeframehastwokindsofslots,namelydataslotsand ontrolslots.
Thedataslotsareusedtotheusertotransmittheirdatawhilethe ontrolslotholdsthe
information forthenext frame'sslotallo ation. Ea hdataslotinaframe anbe
simul-taneously usedbymultipleusers withthe help ofuniquely assigned odes. Whenevera
userneedstotransmitamessage,herstsendsarequestmessagetothe entral ontroller
and enters the ontention pro ess. The ontroller takes into onsideration the time of
generationofa all,thebitraterequirementandthemessagelengthwhilereservingslots
fortheentirelengthofthemessagegenerated. Theuserthengoesinto thetransmission
phaseifheissu essfulinthe ontentionpro ess,and ontinuestotransmithisdatatill
theentiremessageissent. Threes hedulingalgorithmsfortheallo ationofdataslotsare
proposedandtheirperforman earestudiedforfour lassesoftraÆ . Wealsoanalyzeour
proto olusingatwo-dimensionalMarkov hainmodel,and omputethestate transition
probabilitiesandderivetheaveragewaitingtimeforagivensystemload. Bysimulation
experimentsweshowthatourrequest-TDMA/CDMAproto olisabletoee tively
om-binetheorthogonalityofbothtimeand odedivisionmultiplexing. Furtherenhan ements
arealsoproposedtode reasethewaitingtimeandin reasetheaverage hannelutilization.
Keywords: Hybridproto ol,resour eallo ation,TDMA,CDMA.
1. Introdu tion
In thepast twode adesthere hasbeenatremendousgrowthintheeldof wireless
ommuni ations. Theultimategoalistoprovide ommuni ationservi esanywhere,
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
essentialthat the devi e is onne ted to a trans eiver. These trans eivers are the
base stationsina typi al ellularinfrastru ture,where the overage area isdivided
into ells. Ea h ellisserved bya basestation and thebasestationsare onne ted
tothebasestation ontroller(BSC)through ahighbandwidthline whi hisinturn
onne ted to themobile swit hing enter (MSC). The bottlene kin thesetypes of
networksisthe hannel bandwidthbetweenthemobiledevi eand thebasestation.
The bandwidth isjust enough tosustain a full-duplex voi e ommuni ation. Also,
these hannelsarepronetonoiseresultinginhighbiterrorrate. Duetothes ar ity
ofthewireless hannelbandwidth,itisessentialthattheavailablebandwidthisused
asmu haspossible.
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
.
Theavailablebandwidthtoawirelesssystemislimitedandmustsupportamixture
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 ationsgenerallyhavehigherprioritythanthenon-real timetraÆ ,andhen e
they areallo ated asigni antportionof thebandwidth. Whenevertherearemore
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 notonly s ar e butalso expensive. Sin e sharing the limited radio
spe trumresour eisa ommonphenomenoninwirelessnetworks,aneedformedium
a ess ontrol(MAC)proto olarises. Oneof themain onsiderations inthedesign
of a wireless systemis toin orporate multiple a esss hemes 4
thatmakeeÆ 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 topof the existing MACproto ol tosupportsu 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 hasbeenstudied
spreadspe trummultiplea ess (SSMA) omponent aresuperiortoother multiple
a ess s hemes be ause by these te hniques, the frequen y sele tivity of the radio
hannel,whi hseverely impairsthesystemperforman e, anbe averaged out 7
.
Inthis paperweproposea request-TDMA/CDMAproto olforsupporting
mul-timedia 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 forsupportingtraÆ with variousdata rates. This proto ol an be used
asa multiple a esss heme withinone ellof a ellularnetwork. Theresour es are
managed by the base station (s heduler) and are allo ated to the users based on
ertain riteria. The performan eof theproto olis measuredinterms of the
aver-age hannel utilization and theaverage waiting time. Thewaitingtime isthe time
a messagewaitsbeforeitgets areservation. We ondu tsimulationexperimentsto
study and ompare s heduling poli ies whi h are spe i ally designed totake are
of thevariable bitrate requirementsof theusers.
Therestof thepaperisorganized asfollows. Se tion2 des ribestheworkingof
the proto ol. In Se tion 3, we derive the analyti al model. Se tion 4 presents the
s hedulingalgorithmswhileSe tion5summarizestheexperimentalresults. Se tion
6 shows the possibility of further enhan ements and on lusions are drawn in the
lastse tion.
R T S
U
2
1
1
2
3
S
Data Slot 1 Data Slot 2
User 3
User 2
User 1
. . . .
Data Slot S
User U
C T S
FRAME
No. of data slots
No. of Simultaneous Users
Figure 1: Framestru tureof TDMA/CDMA proto ol
2. Proposed Proto ol
Thetwomostimportantaspe tsoftheproposedrequest-TDMA/CDMAMAC
pro-to ol is thedesign of theframe stru ture and thes heduler atthe base station as
des ribed below.
2.1. The Frame Stru ture
kindsof slots,thedataslots andthe ontrol slots. Control slotsarefurtherdivided
intorequest to send(RTS) and lear to send(CTS) slotsasshowninFigure 1.
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
Data Slot 1
Data Slot 2
Data Slot S
Figure2: Code allo ationfor thedataslots
Ea h frame hasS data slots of equal length whi h are used for transmissionof
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
userstosendtheirrequests tothebasestation. Thepro essing of requestsand the
s hedulingaredone during theCTSslots. A CTSslotis divided intoS mini slots,
ea h holding information of the orresponding data slotfor the next frame. Ea h
mini slotisfurtherdivided intoU grids, whereU isthemaximumnumberof users
who an transmit datasimultaneously within a data slot. Ea h of theseU gridsis
initializedwithaCDMA ode (seeFigure2)thatthes hedulerallo atestotheuser
who su eeds ingettinga reservation forthat slot.
In a TDMA system, ea h data slot anbe 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
toall theusers. The odeshave thepropertythat the ross- orrelationamong any
two odes isverylow. We exploitthis orthogonalityproperty 15;2
to a ommodate
multipleusers inonedataslot. The maximumnumberofusers whoare allowed to
transmit theirdata in one slot is restri tedto U as shown in Figure 2. Ea h user
is allo ated a ode bythe CTS. The ode is used totransmit data in oneor more
dataslotsinaframe. Thenumberofdataslotsallo atedperframedependson the
bit rate requirement of the all. The dataslots anbe oftwo types{ reserved and
ompetitive. Thereserved slotsaremeantforaparti ular lassoftraÆ and annot
be a essedbyanother lass,whereasthe ompetitive slots anbea essed byany
lass of traÆ . The numberof reserved slotsis not xedand varies from zero toa
maximum, although the sum of the reserved and ompetitive slots is onstant. A
2.2. The S heduler
Thes heduleratthebasestations anstherequestqueuethathasallthe
in om-ing requests for all establishment along with all the other events o urring in the
system. Therequests ontainingthebitrate requirementsand themessagelengths
are maintainedin the requestqueue 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 transmitmoredata per frame. The lowestbit rate requestis treatedasa single
requestand higherbit ratesasmultiplesof thelowestbit rate. Forexample,if the
requested bit rate is twi e the lowest bit rate then it is onsideredas 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
availabilityof reservedand ompetitive slots.
3. Performan eAnalysis
For the sake of simpli ity, we make ertain assumptions for the system under
onsideration. Wefo usonlyontheuplinktraÆ ,theonesfromthenodes(hereafter
nodes and users will be used inter hangeably) to the base station. Let us assume
that the number of a tive nodes inthe system isN. The duration of a frame isT
se onds and the numberof data slots per frameis S. Therefore, the time of ea h
dataslotis(T C R )=S se onds,whereC andR arerespe tivelythedurationof
the CTSandRTS slots. We alsoassume thefollowing.
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 isrequested is ready. So we ansay that themessages
arrive inwholewitha rate perframe.
A2. In spiteof assumption (A1), thenodes annot generate a new messageuntil
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
messageinthesameframe.
A3. Ea hmessage onsists of a numberof pa kets, and themessagelength
(mea-sured in number of pa kets)follows a negative exponentialdistribution. The
mean messagelengthisL
m .
A4. Anodewhi hhasgenerateda messageinthe urrentframe annot a essthe
data slots inthe sameframe. It hasto wait atleast for thebeginning of the
next frame.
gets a reservation. It might be removed from queue if the waiting message
times outresultingin the all being dropped.
A6. The numberof dataslots that anbe allo ated toa node will depend on the
bitraterequirementofthenode. Thenumberofdataslotsallo atedperframe
remainsxed fortheentirelengthof amessage.
A7. A node after getting a reservation goes intothe transmissionphase and
on-tinues to transmit the entire length of the message. No reserved slots goes
emptyasa onsequen eof assumption(A1).
We onsider m types of traÆ having bit rate requirements in the ratio of 1 :
2 ::m. Let thenumberof data slotsrequired bya node per framebe b,whi h
an take values between 1 and m depending on thebit rate requirement. In other
words,whena node isallo ated dataslots,it willbeallo ated aminimumof1 and
a maximum ofm slots perframeso asto omply withthe minimumrequirements.
As dis ussed earlier, the CTS slothas S olumns and U rows. So, there are SU
(referFigure 2)slots ina frameea hofwhi h antransmitapa ket. Ea hof these
D
S
=SU dataslots are either reserved orunreserved. Let p be theprobability
thatadataslotisunreservedand(1 p)betheprobabilitythatitisreserved. Ea h
of theN nodesinthesystem anbe inoneof thethreepossiblestates;(i)thinking
state, i.e.,thenodeisyettogenerateamessage,and sohasnotenteredtherequest
queue; (ii) ontention state, i.e., the node has generated a message and is in the
requestqueue ontendingtogetareservation;and(iii) reservedstate,i.e.,thenode
has obtainedareservation fortheentiremessageand isunder transmission.
3.1. Markov Model
Thenumberof nodes inea h ofthethree states aregiven below.
N
: Numberof nodes in ontention mode
N
r
: Numberof nodes inreservedmode
N
t
: Numberof nodes inthinking mode
The stateofthe systemwith (N
+N
r +N
t
)=N nodes willnot be ompletely
determinedbyonlyonevariablebe auseforthesamenumberofnodesinthesystem,
there anbevarious ombinationsof thenumberofnodeswaitinginthequeue and
in the reserved state. Asthe number of nodesin the systemis xed to N,we an
ompletely des ribe the state of the system with a tuple having two omponents.
We model oursystem as a two-dimensional Markov hain in whi h a state an be
ompletely representedbythe tuple(N
;N
r ).
Theperforman eofthesystem anbe evaluatedbystudying thedistributionof
thestatevariables. ThesystemisfullyknownattheendoftheCTS,i.e.,attheend
ofea hframe. So,we antakethis pointastheembeddedMarkovpoint. Thestate
frame only. Hen e, the frame boundary is an ideal pla e to represent the system
evolution,asa Markov hain. Letusassume that thestateof thesystem after the
n th frameberepresented by(n ;n r
),and afterthe (n+1) th frameby(l ;l r ).
n
r
l
c
l
r
n
c
State after n frame
th
State after (n+1) frame
th
Figure3: Transitionof onestate toanother
LetA (n)
bethenumberofrequestsforreservation,D (n)
be thenumberofnodes
departing after transmitting theirmessage, and S (n)
be the number of nodes that
are su essful in getting a reservation during the interval between n th
frame and
(n+1) th
frame. So,we have,
l =n +A (n) S (n) (3.1) l r =n r 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 ;N r ). Let N r =n r ,N t =n t and N =n
be the number of nodes in the
reserved,thinkingand ontentionstatesrespe tively. So,we anwritethefollowing
onstraints 0 n r Y =min(D s ;N) 0 n N 0 n t N where D S
=SU is thenumberof dataslots.
3.2. Cardinality of the State Spa e
The ardinalityofthestatespa eisnothingbutallpossible ombinationsof the
tuple(N
r ;N
)withthe onstraintthatn
r +n
+n
t
=N. Thereforeforaxedvalue
of n
, n
r
varying between0 and Y,the possible number of statesthat (n
;n r ) an take isgiven by Y X nr=0 (N n r +1): (3.3)
So the ardinalityof thestatespa e is
(N+1 Y
2
)(Y +1) (3.4)
AsY is upper boundedbyN,the statespa esizeis O(N 2
3.3. Transition Probabilities
InaMarkov hain 11
,ifthesystemis instatei, thenthereisa xedprobability
P
ij
that itwill next be instatej regardlessof the pro esshistorypriortoarriving
at i. We refer to P
ij
as the transition probabilities, whi h satisfy P
ij 0 and P 1 j=0 P ij =1where i=0;1;:::
Reserved Mode
Contention Mode
Thinking Mode
n
r
n
c
n
t
D
S
A
Figure 4: Thetransition probabilities
To al ulatetheelementsofthestatetransitionmatrix, weneedto al ulatethe
transition probabilitiesPrf(n ;n r )!(l ;l r
)g. The transitionbetweenthedierent
modesisasshowninFigure 4.
3.3.1. Probabilityof New Arrivals (A)
Wehaveassumedthatthearrivalrateofmessagesispernodeperframe. Given
that thenumberofnodesinthethinkingmodeisn
t
andtheframelengthisT,the
probabilitythatthere are j arrivals,is givenbythebinomial distribution
A(n t ;j;;T)= n t j ! e T(n t j) (1 e T ) j (3.5)
3.3.2. Probabilityof Obtaining Reservation(S)
In ea h frame there are D
S
slots whi h an either be in a reserved state or in
an unreserved state. Let p be theprobabilitythat a slotis in an unreserved state.
Consider arequestwhi h hasa requirement of bslots perframe. Asingle ode has
tobeassignedtothebslots,whi hee tively meansthatthebslotsshouldbefrom
the samerow(see Figure2). Fortherequesttoget areservation,there mustbe at
leastbunreserved slotsinthesamerow. Therefore, theprobabilityofanodeinthe
ontentionstategoingtothereservedstate, isequaltotheprobabilitythatthereis
atleast onerowwith atleastb unreserved slots. The omplement of thisis tond
the probabilitythat all therows have stri tlylessthan bunreserved slots,whi his
given by p(n 1 unreserved <b)p(n U unreserved <b) (3.6) wherep(n i unreserved
<b)istheprobabilitythatthenumberofunreservedslotsinthe
i th
rowislessthanb. Asthestatusofea h rowisindependent ofthatof theother,
the above expression redu es to [p(n
unreserved <b)℄
U
. The probability of having i
unreserved slots outof S slots is given by S p i (1 p) S i
node does not get a reservation inany of the U rows is obtained by summing the
probabilities of having0 tob 1 unreserved slotswhi h is
b 1 X i=0 S i ! p i (1 p) S i U (3.7)
Theprobability,q,thatarequestwithrequirementofbdataslotsgetsareservation
is thengiven by q =1 b 1 X i=0 S i ! p i (1 p) S i U (3.8)
Thus, forj nodes to go from the ontention mode to the reserved mode, given
that there aren
nodesin the ontention mode,is given by
S(n ;j;q)= n j ! q j (1 q) n j (3.9) 3.3.3. Probabilityof Departures (D)
Tondtheprobabilitythattherearejdepartures,giventhattherearen
r nodes
inthereservedmode,weshouldtakeinto onsiderationtheprobabilityofdepartures
of all lassesof traÆ separately. Let usassume that there are j
i
departures from
n
i
nodesinthereserved modewheren
i
isthenumberofnodesbelongingto lassi,
fori=1;2;;m. So we have n r = P m i=1 n i .
Foranodeintransmissionmodebelongingto lassi,theprobabilityofdeparture
is i L m ,where L m
isthe mean messagelength. If thebase station ankeep a ount
of thenumbermessagesinea h lassundergoingtransmission,thentheprobability
that there arej
i
departuresfrom n
i
nodesinthe reservedmode isgiven by
Pr[j i dep ℄= n i j i ! ( i L m ) j i (1 i L m ) n i j i (3.10)
Therefore, theprobabilityofatotalof jdeparturesfromallthe lasses ombinedis
given by Pr[j dep ℄= X j 1 j m Pr[j 1 dep ℄Pr[j m dep ℄ (3.11)
with the onstraint that j = P
m
i=1 j
i
. We denote the probability of j departures
from n
r
nodesinthereserved modeas
D(n r ;j;L m )=Pr[j dep ℄: (3.12) 3.3.4. Combined Probabilities
We will now onsider all the possible ways in whi h the state (n
;n
r
) an go
l
r n
r
=l where k and l anbe either positive or negative. Depending upon the
valuesof kand l,four asesmayariseforPrf(n
;n r )!(l ;l r )g. Case(i) k0; l0 Prf(n ;n r )!(n +k;n r +l)g= P Z j=l A(n t ;k+j;;T)D(n r ;j l;L m )S(n ;j;q) where Z=min(n ;n t k;n r +l) Case(ii) k0;l<0 Prf(n ;n r )!(n +k;n r l)g= P Z j=0 A(n t ;k+j;;T)D(n r ;j+l;L m )S(n ;j;q) where Z=min(n ;n t k;n r l) Case(iii) k<0;l0 Prf(n ;n r )!(n k;n r +l)g= P Z j=X A(n t ;j k;;T)D(n r ;j l;L m )S(n ;j;q)
where X=max(k;l)and Z =min(n
;n t +k;n r +l) Case(iv) k<0;l<0 Prf(n ;n r )!(n k;n r l)g= P Z j=k A(n t ;j k;;T)D(n r ;j+l;L m )S(n ;j;q) where Z=min(n ;n t +k;n r +l)
3.4. Expe ted Waiting Time
Theexpe ted waiting timeof arequestinthe ontention mode will be given by
(expe tednumberof frames)T,whereT isthe durationofa time-frame. Also,
(expe tednumber of frames)= P 1 i=0 ip i where p i
is theprobabilitythat itwaits
foriframes. We regardtheprobabilityofa requestleaving thequeue afterwaiting
for one frameas p
1
and think of it asthe probability of su ess in Bernoulli trials.
Note thattheprobabilityofwaitingforthese ond frameisindependentof thefa 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
inBernoulli trials statesthat theexpe ted numberof experimentstobeperformed
before su ess is rea hed is 1
p
1
. Therefore, it follows that the number of frames a
requestwaitsbefore leaving thequeue is givenby 1
p1 .
3.4.1. Corre tionTerm
Theaboveanalysisassumesthatarrivals wouldo uronly atthebeginningofa
o ursonlyattheend ofa frame. To makethe orre tion termforthearrivaltime
within a frame, we assume as earlier that the probability of arrival in a frame is
equally distributed over thetime period of the frame. Thus, the expe ted time of
arrivalinthatframeis T
2
. In otherwords,thewaitingtimeintherstframewhi h
weassumed tobeT,is a tually T
2
. So the orre t expe ted waitingtimeis
E(w)= 1 p 1 T+ T 2 = 1 p 1 T 2 (3.13)
Let us now al ulate p
1
. Re all that p
1
is nothing but the probability that a
request does notget a reservation and waits for a time equal to the framelength.
This probabilityhas alreadybeen al ulatedas
p 1 = b 1 X i=0 S i ! p i (1 p) S i U (3.14)
Hen ethe expe ted waitingtime isgiven by
E(w)= 1 P b 1 i=0 S i p i (1 p) S i U T 2 (3.15)
4. Proposed S heduling Algorithms
The s heduler atthe base station s ans through the request queue and tries to
allo ateslotsasrequestedbythenodes. Anode anonlytransmitifitgetsa
reser-vationforthedataslots. Ifthes hedulerndsenoughemptyslotstoa 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 thispro ess ontinuestilltherequestgetsareservationorisfor efullydropped
from the queue. Ea h CTS grid hasa ounter whi h keeps tra kof the numberof
pa ketsremainingtobetransmitted,sothatit anmaintainthereservation tillthe
end ofthetransmission. At theend ofa transmission,the ounterisset to0whi h
implies thatthe ode hasbeenreleasedand it anbe assigned tothenext possible
node, ifany. On e a reservation ismade, thenode has totransmit pa kets and no
freeslotswill be allowed. Thisisdue totheassumptionofbulk arrivaloftheentire
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
reservationisdoneforvarious lassesoftraÆ . Forbrevity,we onsiderfour lasses
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 fordata slots an ontend foranyunreserved slot. The s heduler atthe
base station observesthat ifa node isallo ated multiple data slots ina frame, the
same ode is used,i.e, thedataslots mustbelongto thesamerow.
4.2. S heme 2 : Complete Reservation
In this reservation s heme, data slots are identied for ea h lass of traÆ and
onlytheintended lass anusethe orrespondingreserveddataslots. Themaximum
numberofdataslotsaparti ulartraÆ anhavedependsonthearrivalrateofthat
lassoftraÆ . Weassumethattherequestsfromallthe lassesareequallyprobable.
The reservation madeforthefour lasses onsideredisasshowninFigure 5. It an
be seen that the ratios of reservation for thefour lassesalso follow 1:2:3:4. First,
the s heduler he ks the bit rate requirement (sayb) 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 L
b
e frames, where L is the length of the
message. Therequestwillnotbeallo atedslotsifalldataslotsmeantforthat lass
are alreadyreserved, even ifdataslots forother lassesareavailable.
Resv. for Class 2
Data Slot 4
Data Slot 1
Data Slot 2
Data Slot 3
Data Slot 5
Code 6
Code 5
Code 4
Code 3
Code 2
Code 1
Code U
Code U-1
Resv. for Class 4
Resv. for Class 3
Resv. for Class 4
Resv. for Class 4
Resv. for Class 4
Resv. for Class 4
Resv. for Class 4 Resv. for Class 4
Resv. for Class 4
Resv. for Class 4 Resv. for Class 4 Resv. for Class 4 Resv. for Class 4
Resv. for Class 4
Resv. for Class 4
Resv. for Class 4
Resv. for Class 4
Resv. for Class 3
Resv. for Class 3
Resv. for Class 3
Resv. for Class 3
Resv. for Class 1
Resv. for Class 1
Resv. for Class 1
Resv. for Class 1
Resv. for Class 2 Resv. for Class 2
Resv. for Class 2
Resv. for Class 2
Resv. for Class 2
Resv. for Class 3
Resv. for Class 2
Resv. for Class 2
Resv. for Class 3 Resv. for Class 3 Resv. for Class 3
Resv. for Class 3
Resv. for Class 3
Resv. for Class 3
Figure5: Reservation forvarioustypes
4.3. S heme 3 : Partial Reservation
Theprevioustwos hemeshave ertaindrawba kswithrespe tto ertain lasses
unreserved. Instead,somedataslotsarereservedforea h lassoftraÆ depending
on their relative arrival rates and some data slots are not reserved for any lass.
Theunreservedslots anbeassignedtoany lassoftraÆ whi hdoesnotndslots
from the reserved slots for that lass. On the arrival of a request, the s heduler
rst tries toallo ate slots whi h have been reserved for that lass. If it annot be
a ommodated,thenthes hedulerlookforunreservedslotsfromthe ommonpool.
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 L
m = 50
pa kets. Thisalsomeansthatonanaverage ea hmessagewill require50 dataslots
foritstransmission. Weuseframe-timeastheunitoftime. Wehave onsideredve
data slots ina framewhi h o upy90% of theframeduration and the two ontrol
slots (RTS and CTS) o upy the remaining 10% of the frame duration. One data
slottimeisthetimetaken forthetransmissionofonedatapa ket. MaximalLength
9
odesoflength15wereusedandtherewere15su h odeswhi hwereallo atedto
every dataslot. Therefore, atanytime a maximumof 15 nodes an transmit data
simultaneously. We onsidertheaveragewaiting timeand hannel utilizationasthe
performan emeasures. For hannel utilization,we donot onsider the ontrolslots
and only onsider theutilizationof thedataslots.
Theperforman eofS heme1isshowninFigure[6℄. ItisobservedthatthetraÆ
with higherbit rate requirement were delayed morethan the traÆ with lowerbit
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 eofS heme 2isdepi ted inFigure[7℄where traÆ of lass1
had a onsiderable amount of delay. This is due to theassumption that the mean
messagelengths of all thetypesare sameand lass 1required moretimetova ate
the reserved slots sin e it ould only transmit one pa ket per frame, whereas the
othertypestransmittedmorenumberofpa ketsinaframeandva atedthereserved
slots after the transmission was omplete. So, for thesame mean messagelength,
thenodeswith higherbitratesneededless timeforthetransmission. Asall the64
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 totalof 8 odes (rows) were reserved for the various traÆ
types. The ratioof reservation of ea h lass was basedon the average requirement
forthat lass. Theremaining7 odeswereleftunreservedandany lass oulda ess
it.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
5
10
15
20
25
30
35
40
Arrival Rate (
λ
)
Average Waiting Time (frame)
Class 1
Class 2
Class 3
Class 4
Average
Figure 6: AveragewaitingtimeforS heme 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
50
100
150
200
250
300
350
400
Arrival Rate (
λ
)
Average Waiting Time (frame)
Class 1
Class 2
Class 3
Class 4
Average
Figure 7: AveragewaitingtimeforS heme 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
5
10
15
20
25
30
35
40
Arrival Rate (
λ
)
Average Waiting Time (frame)
Class 1
Class 2
Class 3
Class 4
Average
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.4
0.5
0.6
0.7
0.8
0.9
1
Arrival Rate (
λ
)
Average Channel Utilization
Scheme 1
Scheme 2
Scheme 3
Figure 9: Average hannelutilization forthethree s hemes
termsof hannelutilization. Infa tthe hannelutilizationofS heme3isvery lose
to100%,whi hmeansthatthere wereveryfewdataslotswhi hwerenotallo ated
toanynodeand thuswerewasted. Thereserved slots ateredtheminimumsteady
ow, whereas the unreserved slots were used for the u tuations in thearrivals of
the requestsof dierent lasses.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1
2
3
4
5
6
7
8
9
10
Channel Utilization
Waiting Time (frame)
Class 1
Analysis
Simulation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1
2
3
4
5
6
7
8
9
10
Channel Utilization
Waiting Time (frame)
Class 2
Analysis
Simulation
Figure 10: Performan eof Class 1and 2
Tovalidatethe orre tnessoftheanalyti almodel,we ompareitwithsimulation
results. The omparisonsshown in Figures10-11 isfor S heme 1. For all the four
lasses onsidered,weobtaintheaveragewaitingtimefordierentvaluesof hannel
utilization. Weobservethatthewaitingtimefor lasses1and2areappre iablylow
evenwhen thesystemisloaded. But for lasses3and 4,thewaitingtimeblowsup
when the hannel utilizationsare 0.8and 0.7respe tively.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1
2
3
4
5
6
7
8
9
10
Channel Utilization
Waiting Time (frame)
Class 3
Analysis
Simulation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1
2
3
4
5
6
7
8
9
10
Channel Utilization
Waiting Time (frame)
Class 4
Analysis
Simulation
Figure 11: Performan eof Class 3and 4
mode indenitely. However, in reality, a user might not want to wait indenitely
and would like to try again. Waiting indenitely not only in reases the average
waitingtimebutalso ishighlyundesirable. Thereisgenerallyatimerfun tionthat
de ides themaximumwaitingtimeforajob inthequeue. Ontheexpirationof the
timer, the all isremovedfrom thequeue resultingin 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
errorat thede oderside.
6.1. Introdu tion of Blo king
The performan e of the proposed proto ol with respe t to the average waiting
time anbe enhan ed by introdu ing anexpiration timer. Ifa job is notallo ated
slots within a pre-dened 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 ratioofthe numberof allsblo ked tothetotalnumber
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
initiatedtheexpirationtimer witha pre-denedvalueforea hof thetraÆ lasses.
Themaximumwaitingtimefor lass1, lass2, lass3and lass4were5,15,20and
30 frames respe tively. With these parameters, all others remaining the same, we
have foundthe theblo king probability fordierent values of . We observe from
Figure 12 thede rease in theaverage waiting timeand the orresponding blo king
probability.
6.2. Use of Gold Codes
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
5
10
15
20
25
30
35
40
Arrival Rate (
λ
)
Average Waiting Time (frame)
Class 1
Class 2
Class 3
Class 4
Average
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Arrival Rate (
λ
)
Blocking Probability
Figure 12: Averagewaitingtimeand blo king probabilitywithexpiration timer
there eiver. Inthe aseofML odes,fora ertainlengthLofthe ode,thereexists
exa tly L su h odes. The ML odes have the disadvantage that their number is
limited. This is one of the main reasons tolook fornon-ML odes that do have a
ertain degree of orthogonality. In other words,if we look forsome other types of
ode forwhi h the number of odes available for a ertain lengthof ode is more,
thenmorenumberofusers anbe a ommodatedsimultaneously. Thismeansthat
morenumberofbits anbesuitably oded andtransmitted. GoldCodes 12
aresu h
kind of odeswhi hare obtainedfrom ML odes. Fora ode lengthof L,thereare
L+2 odes. ButtheusageofGoldCodesintrodu essomeerrorbe ausethese 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
antoleratesomeerrors.
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 messagelength was taken tobe 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 tothe use of Gold
Codes.
Fortheparametersdis ussedearlier,weobservefromFigure13thatthe hannel
utilization has in reasedwith the use of Gold Codes as ompared toML odes by
a fa tor of (L+2)=L, with the introdu tion of some errors. The errors o urred
be ausethe odeswerenot ompletelyorthogonal. Thiskindoferrorisusuallyvery
small and anbe toleratedfor voi e ommuni ation. We also nd that the system
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Arrival Rate (
λ
)
Channel Utilization
with ML codes
with Gold Codes
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1
2
3
4
5
6
7
8
9
10
x 10
−3
Arrival Rate (
λ
)
Bit Error Rate (BER)
Figure 13: Channelutilization and BERwiththeuseof GoldCodes
7. Con lusion
We have proposed a new MAC proto ol for supporting multimedia traÆ in
wireless networks. The proto ol uses CDMA laid over TDMAand is hen e alled
request-TDMA/CDMA proto ol. Data slots and ontrols slots make up the time
frames. Ifauserwantstotransmitamessagethenitmakesarequesttothes heduler
whi htriestoallo atedataslotstotheuser. Thes hedulertakesinto onsideration
the time of generation of a all, the bit rate requirement and the message length
while reserving slotsfortheentirelengthofthe messagegenerated. Three
s hedul-ing algorithms are proposed and their performan es are studied forfour lasses of
traÆ whi h have dierent bit rate requirements. We also model ourproto ol
us-ing 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
experimentswe show that our (hybrid) request-TDMA/CDMA proto ol is able to
ee tively ombine the orthogonalityof both time and ode division multiplexing.
Furtherenhan ementsarealsoproposedtode reasethewaitingtimeandtoin rease
the average hannel utilization.
8. A knowledgements
The authorswould like tothank the support of TexasAdvan ed Resear h
Pro-gramgrant TARP-003594-013andTexasTele ommuni ationsEngineering
Consor-tium(TxTEC).
Referen es
1. J.Blanz,A.Klein,M.Nahan,andA.Steil,\Performan eofaCellularHybridC/TDMA
Mobile Radio SystemApplyingJoint Dete tionandCoherentRe eiverAntenna
Diver-sity",IEEEJ.onSele tedAreasinCommuni ations.Vol.12,No4,pp.568-579,May1994.
3. M.ChatterjeeandS.K.Das,\AHybridMACProto olforMultimediaTraÆ inWireless
Networks",IEEEInternationalConferen eonNetworks(ICON)2000,Singapore,pp
30-35.
4. H.S. Chhaya and S. Gupta, \Performan e of Asyn hronous Data Transfer Methods of
IEEE802.11MACProto ol",IEEE PersonalCommuni ations,pp.8-15,O t1996.
5. A.K.Elhakeem,R.DiGiralamo,I.B.BdiraandM.Talla,\DelayandThroughput
Chara -teristi sofTH,CDMA,TDMA,andHybridNetworksforMultipathfadedData
Trans-missionChannels",IEEEJ.onSele tedAreasofCommuni ations.Vol.12,No4,
pp.622-637,May1994.
6. K.S.Gilhousen,I.M.Ja obs,R.Padovani,A.J.Viterbi,L.A.Weaver,andC.E.Wheatly,\On
the apa ityofa ellularCDMA system",IEEETransa tionson Vehi ularTe hnology,
Vol.40,No2,pp.303-312,May1991.
7. P.Jung,P.W.BaierandA.Steil,\AdvantagesofCDMAandspreadspe trumte hniques
over FDMA and TDMA in ellular mobile radio appli ations" IEEE Transa tions on
Vehi ularTe hnology,Vol.42,No.3, pp.357-364,Aug1993.
8. R.O. LaMaire, A. Krishna, P. Bhagwat, and J. Panian, \Wireless LANs and Mobile
Networking:StandardsandFutureDire tions",IEEECommuni ationsMagazine.
pp.86-94,August1996.
9. W.C.Y.Lee,\Overview ofCellular CDMA,"IEEE Transa tions on Vehi ularT
e hnol-ogy,Vol.40,No2,pp.291-302,May1991.
10. G.R.J.Linnenbank,P.Venkataraman,P.J.M.Havinga,S.J.Mullender,G.J.M.Smit,\A
Request-TDMA Multiple-A ess S heme for Wireless Multimedia Networks",
Interna-tional Workshop on Mobile Multimedia Communi ations MoMu -3, New Jersey, Sept
25-27,1996.
11. R.Nelson,\Probability,Sto hasti Pro ess,andQueueingTheory",Springer-Verlag.
12. R.Prasad,\CDMAforWirelessPersonalCommuni ations," Arte h House,1996.
13. K.RavindranandV.Bansal,\DelayCompensationProto olsforSyn hronizationof
Mul-timediaDataStreams", IEEE Transa tions onKnowledge and DataEngineering.Vol.5,
No4,pp.574-589,Aug1993.
14. H. van Roosmalen, J. Nijhof and R. Prasad, \Performan e Analysis of a Hybrid
CDMA/ISMA Proto ol for Indoor Wireless Computer Communi ations," IEEE
Jour-nalonSele ted Areasof Communi ations.Vol.12,No5,pp.909-916,June1994.
15. A.J.Viterbi,\CDMAprin iplesofSpreadSpe trumCommuni ations".Addison-Wesley,