Analysis of GPRS Radio Channel Access DelayShikha Srivastava Subrat Kar

Centre for Development of Telematics Dept. of Electrical EngineeringMandi Road, Mehrauli Indian Institute of Technology

New Delhi - 110030, India New Delhi - 110016, IndiaEmail: shikha@cdotd.ernet.in Email: subrat@ee.iitd.ac.in

Abstract- We present an analysis of delay encountered in responsible for authenticating the user and user services re-successfully accessing the Random Access Channel (RACH) of quested, storing user location information, routing user calls toGeneral Packet Radio Service (GPRS) Radio Interface by mobile the appropriate network and maintaining charging information.stations that want to initiate data transfer. The process of RACHaccess is described and the MS state modeled as a discrete-time II. GPRS RADIO INTERFACEMarkov chain (DTMC) in order to derive the delay. We evaluatethe variation of the radio channel access delay with the maximum GPRS Radio Layer consists of different uplink (890 - 915attempts, inter attempt time interval, number of mobile users, MHz) and downlink (935 - 960 MHz) channels that are furthernumber of backlogged users, radio priority, rate of incoming divided into multiple frequency sub-channels spaced at 200data and rate of retransmissions. The blocking probability or theprobability of complete channel access failure is also evaluated. kHwUlink channel is for MS to BS communication. EaDownlink channel is for BSS to MS communication. Each

I. INTRODUCTION frequency has 8 timeslots comprising a TDMA frame. One toGeneral Packet Radio Service (GPRS) enables users to eight timeslots can be allocated per TDMA frame to one user.

transfer data at rates up to 170 Kbps per user, to and from The GPRS logical channels are as follows: (i) The Packeta network viz. internet or a corporate network. Optimizing Broadcast Control Channel (PBCCH) carries the channelthe radio channel delay will help in improving the network structure and System Information messages for properly ac-performance, give good real time service response and enable cessing and using the network. (ii) The Packet Radio Accessfaster handovers. This paper presents an analysis of the Radio Channel (PRACH) is an uplink channel on which new requestschannel access delay encountered by Mobile Stations (MS). for radio resources are sent by MS. (iii) The Paging ChannelWhen an MS has data to transfer, it must contend with other (PPCH) is used for paging of mobile for incoming packetMSs, to send its request to the network, on a common channel and circuit switched calls. (iv) The Access Grant Channelassigned for this purpose. Slotted ALOHA random access (PAGCH) channel is a downlink channel used for sending re-is the basic access mode. However, in GPRS, even though source allocation information to MSs. (v) The Packet Commona number of mobiles transmit on the same slot, there is a Control channel (PCCCH) is a common channel used for thepositive probability, Capture Probability, of successful packet signaling that precedes call setup. It consists of the PRACH,reception by the network, depending on the power levels PPCH and PAGCH. (vi) The Packet Associated Control Chan-of the transmissions. The situation is compounded by the nel (PACCH) is a bi-directional dedicated control channel usedavailable option of dynamically assigning the random access to send resource assignment messages, acknowledgements andchannels by the network, based on the traffic load. A number power control information during a call. (vii) The Packetof parameters have been defined for minimizing collisions Timing Advance Control Channel (PTCCH) is a channel onand are broadcast as System Information messages. They are which Timing Advance is sent and controlled. (viii) The Packetmaximum retransmission attempts, the minimum inter-attempt Data Traffic Channel (PDTCH) is a bi-directional channel fordelay, inter-attempt spreading factor and access persistence transfer of MS data. It allows independent and asymmetriclevel. channel allocation in both directions.The GPRS network comprises of the Base Station Subsys- The Packet Data Channel (PDCH) is the GPRS Physical

tem (BSS) and Network Subsystem (NSS). The radio coverage Channel. One PDCH is mapped to one timeslot per TDMAarea is divided into Location areas, Routing Areas and Cells. frame. The master PDCH carries all the above logical chan-One Base Transreceiver Station (BTS) serves each cell and nels. The slave PDCH carries only PDTCH, PACCH andprovides the wireless connectivity to MSs. Multiple such BTSs PTCCH. One PDCH may carry multiple PDTCHs belongingare connected to a Base Station Controller (BSC) that does to different MSs.radio resource allocation and management. Many BSCs areconnected to the Network Subsystem.II.ACSPEITNECO RLMDLThe basic network subsystem comprises of the Serving The purpose of the Packet Access Procedure is to establish

GPRS Support Node (SGSN), the Gateway GPRS Support a Temporary Block Flow (TBF) to support transfer of networkNode (GGSN) and the Home Location Register (HLR). It is Protocol Data Units (PDU)s in the uplink direction. The upper

1-4244-0614-5/07/$20.00 ©2007 IEEE.

q q q q q q q TABLE I

1 2X 3 4 5 6; ;, 84XS' PC(t), CAPTURE PROBABILITY

p \? p p 'p p- p' U q t PC (t)1 1.00

SF ~~~~~~~~~~~~~~~~~2 0.673 0.484 0.40

Fig. 1. DTMC showing Transmission State at MS 5 0.35>6 0.00

layers specify the throughput, Radio Link Control (RLC) modeand radio priority associated with the packet transfer. There probability of unsuccessful access. The MS moves from anycan be four radio priority classes {i = 1, 2, 3, 4}. Class 1 of the states 1 to 8 to the state S with probability p. If the MShas the highest priority. RLC mode can be acknowledged or faces channel access failure, it moves to the next higher stateunacknowlegded transfer. Other PRACH Control Parameters with probability q. Say, in case of access failure in the stateare broadcast on PBCCH and include the following access 2, MS moves to state 3. In state 8, all attempts are over andpersistence control parameters as in [1]:- the MS moves to state F with probability q in case of access

* Access Control Class is a bitmap for 15 access classes, failure.indicating whether MSs belonging to that class can accessthe PRACH. IV. DELAY MODELING

* M or MAX-RETRANS indicates the maximum number The model assumes that the PRACH channel is fixed andof retransmissions allowed. It is defined for each Radio not dynamically changing, the response for channel allocationPriority Class. M = {1, 2, 4, 7}. is immediate, the packet call arrival at the mobile is a Poisson

* P(i) or PERSISTENCE-LEVEL indicates the ac- process and all mobiles belong to the same radio priority class.cess persistence level for each Radio Priority Class.P(i) = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16}. A. Channel Access delay

* S is the minimum number of time slots between Consider Nm mobile stations, out of which Ni are idletwo successive Packet Channel Request messages. users and Nb are backlogged users. A backlogged user is oneS = {12, 15, 20, 30, 41, 55, 76, 109, 163, 217}. whose previous attempts of channel access have failed. Each

* T or TXINT randomly spreads the gap between idle user transmits independently in each slot with probabilitytwo successive Packet Channel Request messages. h. Each backlogged user transmits independently in each slotT = {2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 20, 25, 32, 50}. with probability b. Let I(Ni, Nb) be the probability that Ni

Let us consider a cell with multiple GPRS MSs. The Uplink idle users attempt to transmit in a slot when there are Nbchannel access procedure for a mobile station(MS) is modeled backlogged users, B(Ni, Nb) be the corresponding probabilityas follows: for backlogged users, d the random variable representing the

1) Data arrives at the MS with rate Ad number of data packets arriving at the MS, Ad the Poisson2) It selects a random value R from a uniformly distributed distributed packet call arrival rate at the MS in packets/ms,

set {0, 1,..., ,14, 16}. Pd be the probability that the idle mobile has data to transfer,3) If R > P(i), MS accesses the RACH. P1 be the probability that the backlogged user transmits, Pa4) The MS sends Packet Channel Request message on the the probability that the MS accesses the channel, P(,)max the

PRACH corresponding to its PCCCHWGROUP and starts maximum P(i) value and Pin the number of possible P(i)a 5 sec timer at the first attempt. values.

5) The MS accesses the channel again after a certain num- Axber of TDMA fames whose value is selected uniformly p(d = X) d e-Ad (1)from {S, S + 1, ... S + T- where X -0,, 2, 3,... is the number of packet calls.

6) MS accesses the channel until it gets a response forthe Packet Channel Request message or the maximum Pd 1 -p(d = 0) (2)number of attempts are over or the 5 sec timer expires. Pa P(R > P(i))After that it stops the access. P(i)ma - P(i) + 1

Let the value of M = 7. The average number of attempts per PtnMS can be modeled as a discrete-time Markov chain (DTMC) h Pd Pa (4)with two absorbing states, as given in Fig. 1. The number...of transmission attempts denotes the state of the system. The Temnmmrt twihrtasisosaecridotbstate S denotes successful access and state F denotes complete a backlogged mobile [2] isfailure of the channel access process. They are both absorbing 1states. p is the probability of successful access. q is the A1. (S+T -1) pcesm 5

where Tts is the duration of one timeslot in ms. The probabilitythat the backlogged mobile generates Y packets (6 100

A> -

As in [3], [4] packet is stuccessfully transmnitted in a stlot | .32if (1) Only one idle user transmits and no backlogged usertransmits, (2) Only one backlogged user transmits and no idle 50 100 150 200user transmits. The probability of successful channel access p S'N.o ielt btentoatmtiS given by Fig. 2. Variation of E(V) Inter-Attempt Delay with S, T

p =I1, Nb * B(, Ib+I(O, Nb (,N) (7)

However, in GPRS the capture probability determines the 1 r=Xtpacket success rate [5]. It is the probability of receiving data ol.correctly if more than one MS transmits in the same slot due to ,the greater power level of the said MS. The Table I shows the o -/ <PC(t) or capture probability values for a particular t from [5]. tis the number of MSs transmitting at the same time. Therefore, O 0.001 P=10for GPRS, the probability of successful channel access is given N.0.000 Pa=0.i3p5bygv bi2 ato Pay0.1875 T

p = 1(1, Nb) B(O, Nb) + 1(0, Nb) B(1, Nb) 0.001 0.01 0.1 1 105 t incoming data rate (packet calls/ins)

+ ZPC(t)ZEI(t,Nb) B(t-z,Nb) (10)t=2 z=0 ~~~~~~~~~~~~~~~Fig.3. Variation of h with Pa, Ad

The probability of unsuccessful channel access q is given by

I(t, Nb) = A >l(2t1 ~ ~ ~ ~ (2 J(1, :) =[ P1 P2 P3 P4 P5 P6 P7 P8 ] (19)

B(t, Nb)= 2 . e A2 (13) Given the average number of channel access attempts, if theAl1 Ni h (14) inter-attempt delay is estimated, then the total channel accessa2 Nb b (15) delay can be obtained. The channel access delay T can be

The state transitions of the MS as shown in Fig. 1 can be give by(captured in the state transition probability matrix P [4]. QrTiVul+rVt +r+mV[ (20)is a 8 x 8 substochastic matrix capturing the transient state where Vi is the random variable representing the inter-attempttransitions only. C is a 8 x 2 column vector, 028 is a 2 x 8 time interval and v is the random variable representing thevector of zeros andM 2 is a 2 x 2 identity matrix. J is the numberofattempts.TheaverageE(V) oftheaboveuniformsolution matrix whose first row J(1,:) gives the steady state distribution gives the average inter-attempt delay of an MS.probabilities of MS for being in a particular state.

0 q 0 0 0 0 0 0 p 0 E()S+(S+1)++-X(S+T 1) (21)

000qOOOOpO 8~~~~~~~~~~~~~~.00 P=.47

00 0 0 q0 0 0 0 p 0| E(v) ZEi.Pi (22)

P = I~ON) BOOO OqOp O (16) E(T) = E(Vi) E(v ) (23)0 0 0 0 0 0 0 q p 0 Pb, the blocking probability is the probability that the user0 0 0 0 0 0 0 0 p q completely fails to access the channel, given that user starts0 0 0 0 0 0 0 0 1 0 in State lis given by [4], [6]

A JC (24)0 °28 I2 ] (17) Pb = A(1,2) (25)

S 12 S 12,Pa 1.0,h0.0002,b0.124

0.1 Pa--1.01Pa--0.43750.Pa0.1875

Pa--0.0625

0.01 ~~~~~~~~~~~~~~~~~~~~~0.010.01~ ~ ~~~~~~~~~~~~~~~~~~.0

o0v 0.001

4 0.001 0.0001-; 0.01 0.1 5 10 15 20 25 30 35 40 45 50

retransmission rate (packets/ms) Nb, No. ofbacklogged users

Fig. 4. Variation of b with Pa, A, (a)

S 12, Pa 1.0, h 0.0002, b 0.124, Nb 0.2Nm

S= 12,Pa= 1.0,Nm 25,Nb 9

; 1 0.1ct 0.1b= Nm, No. ofmobileusers0.027

-~~~~~~~~ ~~~b=0.039b=0.053 0.01

0.096b~~ 124-.---- ~~~~0.001

0.00010 100 200 300 400 500 600 700

Nm, No. of mobile users0.10.001 0.01 0.1 1 (b)

h, prob of access by idle user

(a) Fig. 6. Variation of p with (a) Nb and (b) Nm

S 12, Pa 1.0, Nm 25, Nb 9

V. NUMERICAL RESULTS

From Fig. 2, it is seen that E(V) increases as S and T10 increase. Its minimum value is 7 ms and maximum value is

--------- ~~~~~~~~~~154ins.o X000. f x ia b= ^ Probability h of successful channel access by an idle user

,^ X0 0 0 fi ,078 2depends on Pa and on Ad, rate of incoming data. Predictably,=0.096 0 000-Xasthe P(i) value increases and thereby Pa decreases, h

o.()01 001 z ).1 1 decreases gradually. As seen in Fig. 3, h increases gradually0.001 0.01 0.1 1h, prob of access by idle user as Ad and Pa increase.

(b) Retransmission rate Ar decreases with increase in S, Tvalues and the probability of successful access for a back-

S 12,Pa 0.0625 logged user, b increases with increase in Pa and increasesQ 1 with increase in Ar as shown in Fig. 4.

The effect of b and h on the value of p can be seen in

i o0.1 Fig 5. From Fig. 5(a) for Pa = 1,Nb = 9 as h increases, pincreases gradually and then decreases for a particular value of

o ==X:b-0.027 g b. p increases with increase in b. p is not 1.0 which shows that: 0.o01 b=0.053 access failure can occur. When h = 1, p is not high, showing

b=0.096 that even though idle user definitely accesses the channel,_________________________________.1 success is not guaranteed. When Nb increases, p increases

0.001 0.01 0.1 1 for h = 1. Fig. 5(b) shows the number of attempts for theh, prob of access by idle user same b, h values. As p falls number of attempts increase and

(c) as it peaks, number of attempts fall. Fig. 5(c) shows that as Pa

Fig. 5. (a) Variation of p with b, h for Pa =1.0 (b) Variation of E(v) no decreases, both b, h decrease and p increases. p also dependsof attempts with b, h and (c) Variation of p with b, h for Pa =0.0625 on Nm and Nb. For Pa =1.0, h =0.0002 and b =0.124,

p increases gradually with Nb and then falls gradually afterpeaking as seen in Fig 6(a). Fig 6(b) shows that p decreasesas Nm increases.

7~ 0.1

3 100C) 0.01

E(V)=14.42E(V)=10.04 -

E(V)=10.6 2~~~~~~~~~~0.001E(V)=13.06

; 10 0.00010.0001 0.001 0.01 0.1 0 100 200 300 400 500 600 700

p, probability of successful channel access Nm, No. of mobile users

(a)Fig. 8. Variation of Pb with Nm

S 12, Pa 0.0625, Nm 50, Nb 25, M 7

time slots between two successive attempts, M, maximumretransmissions, Ad, rate of incoming data, Ar, rate of retrans-

1 E 1loo missions. S and T affect E(V) and Ar. Ar is higher than AdE(V)=10.04 for low values of S, T. In such a case, probability of accessE(V)= I0.6 adscesi o sr h

V ~ E(V)=13.06 and success iS higher for a backlogged user. The probabilityE(V)= 6.38 = of successful access for idle user is high only when number of

P ~~~~EV)=21.5 hig10l backlogged users is less. In order to keep the channel access0.01 0.1 1 delay low, the values of S should be small. However, even with

p, probability of successful channel access'the largest values of S, E(V) comes out to be 150 ms and

(b) would be reasonable for M = 2. M along with p determinesS 12, Pa 1.0, Nm 50, Nb = 25, M = 2 the success rate of the channel access. While choosing the M

value a compromise has to be struck between the delay andE(V)=14.42E(V)=10.04 the probability of success in access. Nm, Nb, Pa, A, and Ad

7r 0E(V)=10.6 affect p. Capture effect increases p. Lower the Pa, greater the p

E(V)=16.38. and lesser delay. p and in turn the average number of attempts100 E(V)=1.58e _ affect the delay. The parameters which contribute most to the

x E < delay would be p, probability of successful channel accessv : : = = and E(V), the inter-attempt delay. The blocking probabilityP ________________ increases for low M and large values of Nm and Nb. It

0.0001 0.001 0.01 0.1 decreases with decrease in Pa.p,probability of successful channel access

(c) ACKNOWLEDGMENT

The authors would like to thank Dr. S.Dharmaraja, AssistantFig. . Variation of E(T) access delay with p, E(V) for (a) M = Pa= Professor and Vaneeta Jindal, Research Scholar of Department

of Mathematics, Indian Institute of Technology, Delhi for theirvaluable feedback and help.

E(T) is directly proportional to E(V). As p increases, REFERENCESinitially E(T) remains constant, it then decreases as in Fig 7(a) [1] "Digital cellular telecommunications system(phase 2+); General Packetfor S = 12, Pa = 1 and Fig 7(b) for S = 12, Pa = 0.0625. Radio Service (GPRS); mobile station (MS)-BSS interface; RadioAs seen in Fig 7(c) the decrease in M or maximum Link Control/Medium Access Control (RLC/MAC) protocol (GSM

retransmissions decreases the total access delay E(T). It also 04.60)," European Telecommunications Standards Institute (ETSI), avail-able:http:Hlwww.etsi.org/.decreases the probability of channel access success. [2] D. Raychaudhuri and K. Joseph, "Performance Evaluation of Slotted

Fig 8 shows that the blocking probability first decreases and ALOHA with Generalized Retransmission Backoff," in IEEE trans. onthen increases with increase in Nm, For low P(a) it decreases Comm., vol. 38, no. 1. IEEE, Jan 1990, pp. 117,122.

[3] D. Bertsekas and R. Gallager, Data Networks. Pretince-Hall, 1992.gradually with increase in Nm. With increase in Nb, blocking [4] K. S. Trivedi, Probability and Statistics with Reliability, Queuing, andprobability is higher. Computer Science Applications. John Wiley and Sons,Inc., 2002.

[5] R. Robertson and T. T. Ha, "A Model for Local/Mobile Radio Communi-VI. CONCLUSION cations with Correct Packet Capture," in IEEE trans. on Comm., vol. 40,

The channel access delay depends on a number of pa- [6] J. Medhi, Stochastic Processes. Wiley Eastern Ltd., New Delhi, India,rameters like Nm, number of mobile users, Nb, number 194of backlogged users, P(i), access persistence level, 5, T,