Traffic capacity of cellular mobile communications systems

447

Traffic Capacity of Cellular Mobile Communications Systems

D a v i d E V E R I T T School of Information Technology and Electrical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia

Abstract. In a cellular mobile communication system, the traffic capacity of the system is an important quantity, and depends on the way that channels are allocated to calls. Many channel allocation algorithms have been proposed, and this paper makes a direct comparison of some of them. Specifically, the operating regimes considered are fixed channel assignment, dynamic channel assignment, directed retry, and directed handoff. The main conclusion is that directed handoff gives a strong gain in traffic capacity and traffic adaptability for these systems.

The paper also discusses some of the factors affecting the future development of mobile communication systems.

Keywords. Cellular telephony, directed retry, directed handoff, dynamic channel assignment.

David Everitt received the degrees of B.E. and Ph.D. in Electrical Engineer- ing from the University of Queens- land, Australia in 1976 and 1981 respectively. From 1981 to 1986, he worked at the British Telecom Re- search Laboratories, and from 1987 to 1988 worked at the Telecom Australia Research Laboratories. Since March 1989, he has been a Senior Lecturer in Electrical and Electronic Engineering at The University of Melbourne. His interests are in the performance

evaluation of communication networks, especially with regard to cellular mobile communications systems, and to local area networks.

North-Holland Computer Networks and ISDN Systems 20 (1990) 447-454

1. Introduction

Mobile communications systems are the telecommunications systems of the future. They free the user from being tied in a communications sense to one particular location, allowing the free movement of physical location while retaining a constant communicat ions address (telephone number). Mobile communications covers the tech- nologies of cellular mobile communications systems, satellite mobile, portable hand-held systems, cordless telephones, and the wireless office. This paper is concerned primarily with the application to cellular mobile services, but the future direction of technology appears to be towards an amalga- mation of these systems into a single "universal personal communications service".

The idea behind a cellular mobile telephone service is that the service area is divided up into a number of different cells, which are usually drawn for convenience as hexagons. Then, a radio base station is erected in each cell, and this base station will handle all calls made by mobile customers within its geographical coverage area (hexagon). The distinguishing feature of the cellular service is that a radio channel may be used simultaneously in a number of physically separate cells, de- termined by interference constraints. Therefore, it will be impossible to use the one channel simultaneously in adjacent cells, but it may be possible, for example, to reuse a channel in any non-adjacent cell. This leads to the concept of a reuse group. A reuse group is a set of adjacent cells such that the use of a particular channel in one cell precludes its use in any of the other cells of the reuse group. Existing cellular systems typically have a reuse group of 7 cells. This means that, for example, if we have a system with say 350 channels available, and assuming that cells all have the same traffic demand, we can allocate 50 channels to each cell.

The other main idea in cellular systems is that of handoff. This happens when a mobile customer crosses a cell boundary during the course of a call,

0169-7552/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

448 D. Everitt / Cellular mobile communications systems

and as a result suffers deteriorating speech signal quality; the system will then attempt to allocate the subscriber a new channel in the new cell. This assignment of a new channel is termed handoff.

The method of assigning channels to cells and to calls is an important feature affecting the ef- ficiency of cellular systems. The simplest method (and that used in current systems) is fixed channel assignment, where channels are assigned perma- nently to cells according to the long term traffic load in that cell, and calls within that cell boundary can use only those channels previously assigned to that cell.

At the other extreme is dynamic channel assignment, where all the channels form a pool, and are allocated to cells as required by the real time traffic load in that cell. Such assignment methods can significantly increase the traffic capacity of such a system, especially when reassignment is used, i.e. when calls can have new channels assigned to them during the course of a conversa- tion, even when they have not crossed a cell boundary. A particular benefit of dynamic channel allocation methods is that the system can adapt to time varying traffic parameters, i.e. when the spatial traffic profile changes due perhaps to vehicular traffic congestion, or perhaps simply due to all of the mobile subscribers rushing towards the central business district in the morning rush hour. Thus dynamic channel assignment allows real-time network traffic management of a cellular system. The disadvantage of dynamic channel assignment is that its physical implementation re- quires a great deal of processing power to de- termine optimal allocations, and a heavy signal- ling load on the system to implement all the channel changes.

In between the extremes of fixed and dynamic channel assignment, there are many possible alter- natives, including hybrid schemes, and schemes such as directed retry and directed handoff, which take advantage of the fact some percentage of the mobile stations may be able to obtain sufficient signal quality from two or more cells. With directed retry, if a call finds its first attempt cell has no free channels, it can then try for a free channel in any other cell which can provide sufficient signal quality. Directed handoff takes this idea further, in that, when a cell has all or almost all of its channels in use, it may, using directed handoff, direct some of the calls currently in progress in

that cell to attempt to hand off to an adjacent cell. The motivation here is to attempt to redistribute calls in heavily loaded cells to adjacent cells when these adjacent cells are temporarily carrying a lighter load due to statistical fluctuations in the cell traffics.

Both directed retry and directed handoff would therefore be expected to improve the system performance. This improvement would be dependent on the percentage of calls which can hear multiple cells simultaneously; this percentage has been quoted as being perhaps as high as 30-45%. Here, we report on a comparison between these schemes. The salient features of our investigation are that we compare against an upper bound for dynamic channel allocation schemes, rather than a realisa- tion of some particular algorithm. Furthermore, we attempt to compare these schemes in terms of their ability to adapt to time-varying spatial traffic profiles (the network traffic management problem).

During the remainder of this paper, directed retry and directed handoff are sometimes referred to simply as DR and DH respectively. The percentage of calls which can hear two cells simultaneously will often be referred to as a percentage overlap, with the connotation being that of over- lapping cells.

2. Methodology

The method used for the comparisons of this paper is purely simulation. Some analytic ap- proximations are available for such systems [5,10,12], and some simulation results are given in [1]. However, for a comparative study it seems more reasonable to use a consistent procedure between systems, so that we can be sure that the same system is being modelled in each case, and so that approximation inaccuracies do not affect the results.

For dynamic channel assignment, we use the generic dynamic channel assignment algorithm of [7]. This algorithm, called the maximum packing, or MP algorithm, gives the general properties of a dynamic algorithm, without having to model specific details of any algorithm. Moreover, it provides a bound on system performance, giving the best that can be achieved from dynamic allocation algorithms. The basic assumptions used are

D. Everitt / Cellular mobile communications systems 449

the same as those used in earlier papers [7,8]. They are - the cell offered traffics are Poisson, - blocked calls are cleared and do not return, - there are no restrictions (other than frequency

reuse) on channels used by any mobile or any cell,

- t h e effects of fading and co-channel interference are not modelled,

- mobile to mobile calls are ignored, - no account is taken of the movement of the

mobile subscribers between cells for call handovers. The additional assumptions required for mod-

elling directed retry and directed handoff are - within a cell, calls are spread uniformly over the

area of the cell, - there is some specified probability that a call

can hear two cells simultaneously. The probability of hearing three or more cells will be ignored,

- once a call experiences directed retry or directed handoff into an adjacent cell, it is considered to behave as if it were a call which originated in that adjacent cell. This can obvi- ously only be an approximation to the real system behaviour: however, it does not seem unrealistic in that a call which has been handed to an adjacent cell is near a cell boundary, and would be likely to cross that boundary "soon", and so become physically located in that adjacent cell.

Fig. 1. L a y o u t fo r 49 cell sys tem.

0.25

0.20

D FLxed • F~xed with directed ngry

- 30% overlap • FJ.xed , , v i ~ dL'~cw, d ~

- 100% overlap 0 Dynamic (NIP)

- no overlap

0.15 .!

0.10

0.05

0.0 ~ ~ T i l i 35.0 40.0 45 .0 50.0 55.0 60.0

Tra t~ per ten (E.rhngs)

Fig. 2. F ixed vs f ixed wi th d i r e c t e d r e t ry vs d y n a m i c , 49 cells in

t w o - d i m e n s i o n a l torus , 350 channe l s .

The specific algorithms used for directed retry and directed handoff are described in the follow- ing section, along with some numerical results.

3 . N u m e r i c a l R e s u l t s

The system that is used for numerical comparison is a homogeneous 49 cell system with 7 cell reuse groups. In order to eliminate the influence of edge effects, the artifice of e.g. [13,15] has been used. That is, the cells are arranged so that they effectively form a continuous toroidal surface. This arrangement is shown in Fig. 1. The number of channels is assumed to be either 350 channels (i.e. 50 channels per cell for fixed assignment) or 700 channels (100 per cell).

3.1. Directed Retry

We begin by comparing directed retry with fixed channel assignment and with dynamic channel assignment. This is done in Fig. 2 for a total of 350 channels, and in Fig. 3 for 700 channels. We see that the performance of directed retry does not approach that of dynamic channel assignment un-

450 D. Eoeritt / Cellular mobile communications systems

0.25

D Fixed • r-~x~ witll c l ~ ,,~

- 30q. oveztap 0.20 • F i xed w i l b directed

- 100% overlap o Dm~,mi= (MP)

- no ov(= lup

0.15 I m

~ 0.10

0.1~ / / _

0.0 i 70.0 80.0 90.0 10(3.0 110.0 120.0

Tntffic per cell (F.rlangs)

Fig. 3. Fixed vs fixed with directed re t ry vs dynamic , 49 cells in

two-dimensional torus, 700 channels.

less there is the possibility that almost all mobiles can hear two cells simultaneously.

The form of directed retry used above assumes that a directed retry occurs only if all channels in the original target cell are already in use. We might also consider the addition of some threshold, say t, to this strategy, where, if an arriving call finds or fewer free channels at the target cell, a directed retry will be attempted. The idea of using these thresholds is that the traffic can begin to be "evened out" over the cells before a cell becomes full.

The specific algorithm that has been evaluated is as follows:

1. If there are t or fewer free channels at the original cell, then attempt a directed retry.

2. Then, if the second choice cell has some free channels, the call is carried at the cell with the largest number of free channels.

This can be made more explicit mathematically as follows: Assume, e.g., that the first choice cell is cell 1, and the second choice cell is cell 2. Let the number of free channels at cell j be mj for j = 1 or 2. Then, for a new call arriving at cell 1,

0.25

0.20

0 . 1 5

0 . 1 0

0.05

0.0

o F~i

• F~d ~ d~c~d retry - 30q~ ove~hlp , t h r e ~ o l d = 0

• F~ed with directed reuy - 3 0 % ore:drop, lh. . , '~aold - 1

• Fix ~ with dit~--t~ x'~a'y - 30% ov~lap, threshold - 2

A Fixed with directed ferry - 30% ovq~lmp, threshold = 5

o ~ c (~P) - n o ovea, lmp

3 5 . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 . 0 6 0 . 0

Traff'~ per cell (Erlangs)

Fig. 4. Fixed with di rected re t ry and thresholds, 49 cells in

two-dimensional torus, 350 channels .

If m a > t, carry the call at cell 1, 0 ~< m~ ~< t and m 2 > m 1, carry the call at cell 2, 0 < m a ~< t and ml > m 2, carry the call at cell 1, m~ = 0 and m 2 = 0 , the call is blocked. Results are given in Fig. 4. We see that some

improvement results from the use of these thresholds, but the changes are really "fine tuning". It should also be noted that the increased capacity here is at the expense of increased radio interference throughout the system.

3.2. Directed Handoff

Further improvement can be obtained from the use of directed handoff. With directed handoff, we can attempt to even out traffic throughout the system by moving existing calls, as well as just new calls as in pure directed retry. The specific algorithm that has been tested is as follows:

1. When a new call arrives, use directed retry as above.

2. If the new call would be blocked by the directed retry algorithm, then attempt some directed handoff.


0.25

0 Fxxcd

• F*x~l witla ~ ~ l - 30% overlap /,

0.20 • F ixed w k h diz, ec'ted zecty and handof f / ) - 30% ovexlap / / I

• nqnamic (ivy,) with ~ ~ and h, ndo~r / / - 30% ovealap / / /

o D ~ (m~ // / ,I,

0.15 - no owrlap / / / /

w

0.10

0.05

0.0

35.0 40.0 45.0 50.0 55.0 60.0

Tra£fic pea" cell (E~langs)

Fig. 5. Fixed with directed retry and directed handoff, 49 cells in two-dimensional toms, 350 channels.

3. The directed handoff algorithm chooses the adjacent cell with the greatest number of free channels, and then attempts to find one call in its own cell which can hear this adjacent cell. If such a call can be found, then this call is handled off to the adjacent cell, and the new call is carried at the original cell; otherwise the new call is blocked.

Some results are shown in Fig. 5. We see that this can offer a significant improvement over the case of dynamic channel assignment with no overlap. For dynamic channel assignment with overlap, and operating with directed retry and directed handoff, we see that the operation is extremely similar to fixed channel assignment operating with directed retry and directed handoff. That is, dynamic channel assignment appears to offer no improvement over fixed assignment in such cir- cumstances (at least for the case considered).

The simulation results also seem to suggest that dynamic channel assignment with DR and DH may perform slightly worse than fixed assignment with DR and DH. This is probably simply due to the particular directed retry algorithm being used here. A more sophisticated algorithm may be re-

quired in conjunction with the dynamic assignment.

3.3. Traffic Adaptability

A further issue is that of the ability of the channel allocation algorithm to adapt to the un- known traffic parameters of the system. This has been considered for dynamic channel assignment in [8]. The same methodology as in that paper is used here to study the adaptability of algorithms using fixed channel assignment with both directed retry and directed handoff.

The methodology is as follows: Assume that the total system traffic is known

(as would be monitored in the mobile switching centre), but that the mean traffic demands in individual cells are not known, but are char- acterised by some distribution function. Also assume that all cells are statistically identical, in order to reduce the dimensionality of the problem. Traffic variability is modeled by assuming that the mean traffic in each cell is a normally distributed random variable, with a given mean and variance.

To be mathematically precise, assume that the system has m cells, and that the total system traffic is required to be m .A . Denote the traffic offered to the ith cell by A, We choose m independent random variables A~ from a normal distribution with mean A and the given variance. Then the traffics A i are calculated by normalising the A~to give the desired total system traffic:

mA A i = A~' m

! A, i - 1

Results are given in Fig. 6. Each point on each curve was produced with 200 independent choices of the spatial traffic distribution. Three curves are shown in each graph. The curves represent the blocking probability for the system dimensioned to a nominal grade of service as if the mean traffics in each cell are known and constant.

We see the result that the algorithms using directed retry and directed handoff are significantly more adaptable than dynamic channel assignment (without overlap). It should be empha- sized that each of these curves is for a different traffic level, and so it is really only the sensitivity properties which are illustrated.

0

0 oFixed-44.54 E/cell average

• Dynamic - 0% overlap - 49.0 E/cell average

oFixed with dr and dh - 10% overlap - 48.4 E/cell average

aFixed with dr and dh - 30% overlap - 51.9 E/cell average

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.0


o.o o11 o~ o~ oi, 0.5

Coefficient of variation of traffic per cell Fig. 6. Blocking probabilities, 49 cell torus, 350 channels, 5% nominal grade of service.

We see that, if 30% of calls can hear two cells simultaneously, the system could carry more traffic, and be less sensitive to traffic variations, than a system operating with dynamic channel assignment, but where there is no overlap between cells. However, at 10% overlap, this is no longer true. The conclusions are therefore very dependent on the actual percentage of customers which can hear multiple cells.

3.4. Conclusions

In this section, a direct comparison between fixed channel assignment, dynamic channel assignment, directed retry, and directed handoff. The main conclusions are - Directed handoff algorithms have very good

sensitivity properties with respect to variation in the spatial traffic profile of the system,

- directed retry improves system performance. The inclusion of thresholds in the directed retry algorithm improves this performance by only a small amount,

- directed handoff has the capability to offer a very large increase in system performance, if a significant number of calls can hear two or more cells simultaneously.

4. Future D i r e c t i o n s

Current cellular mobile systems are analogue, but the evolution to digital radio systems is being planned for within the next few years. In particular, a pan-European standard has been agreed for a digital cellular system using narrowband time- division multiple access (TDMA) bearers. Digital technology enables the use of high-density mobile services by supporting low-cost terminals, and by increasing bandwidth utilisation (and hence traffic capacity). In order to support these high subscriber densities, very small cell systems are being planned [4,9,11].

Small cell systems are interference limited, and the handover boundaries between neighbouring cells are very difficult to predict in high density urban systems. This means that the cell layout and radio-reuse patterns are very difficult to plan. To maintain high utilisation of the available radio channels in this environment, therefore, some form of flexible channel /cel l assignment becomes virtu- ally essential, with the ability to assign radio channels to different cells within the reuse constraints (flexible channel assignment) or to assign calls to channels in different cells (flexible cell assignment) in order to help match radio base station


capacity to the real-time spatial traffic load. This may be either dynamic channel assignment, or some load sharing algorithms such as directed retry and directed handoff.

However, dynamic channel assignment is very difficult to implement even for current size systems, since it involves a requirement that the channels in use at each cell are known at some central site, which can then perform some optimis- ation and reassign channels between cells and mobiles. This makes the processing requirements extremely large. To try and get around this large processing load, a form of "decentralised" dynamic channel assignment has been proposed, particularly for cordless telephone systems [2]. The idea here is that channels are not assigned centr- ally, but instead, when a call is set up, the mobile scans through the available channels measuring the quality of the channels, and then chooses a channel which satisfies some quality constraints. Such an idea is easily adapted to the mobile situation, and some simulations of such a decentralised algorithm have been reported in [3]. The attraction of this scheme is that the mobiles now have the responsibility of assigning their own channels, so there is no longer the huge system overhead of a centralised dynamic allocation policy. As yet, there are no analytic means of evaluating such systems. We might argue that a "well designed" decentralised system will arrange itself into some stable reuse pattern with some equivalent reuse group, and then the earlier results for centralised dynamic channel assignment could be used. A great deal of further work will be required in order to properly analyse these systems, and in particular, the stability of the algorithms used will be very important.

Another important issue in cellular mobile systems is the determination of a suitable traffic reference model for traffic studies. The numerical results in this paper were produced using an even spatial traffic profile, but this is not realistic. We need some model with a peak in the central business district, but the question is how quickly the traffic should decrease outside of this. Some non- uniform traffic profiles have been suggested in [14], and these may prove to be a good starting point. In addition to the spatial traffic profile, some standard method of describing the mobility of subscribers is needed. This mobility affects the handoff rates in the system, and will induce some

correlation between the traffic loads in adjacent cells. This mobility aspect becomes increasingly important as cell sizes decrease towards a micro- cellular system.

To summarise, it is important to be able to evaluate the traffic performance of these new small-cell systems, particularly with dynamic channel assignment, in order to provide analytic techniques that can form the basis of traffic di- mensioning algorithms for future cellular mobile networks.

Acknowledgment

The majority of this work was performed while the author was employed by Telecom Australia Research Laboratories. This work described here has benefitted from discussions with colleagues in Telecom, particularly Reg Coutts, John Campbell, and David Manfield. The permission of the Ex- ecutive General Manager, Telecom Australia Re- search Laboratories, to publish this paper is hereby acknowledged.

References

[1] O.A. Allavaneda, R. Pandya and G. Brody, Traffic mod- elling of a cellular mobile radio system, in: M. Akiyama, ed., Proc. 11th Intern. Teletraffic Congress, Kyoto, Japan, (North-Holland, Amsterdam, 1985) 2.4B-4-1-7.

[2] F. A1-Salihi and L.P. Strauss, Simulation of cordless communication systems, Electron. Lett. 24 (12) (1988) 742- 743.

[3] R. Beck, F.W. Ho and H. Panzer, Dynamic channel assignment in radio communication networks with micro- cells, DigiMATS Australia, Stage 3, Final Report, R&D investigation of digital mobile radio telephone systems (Telecom Australia Contract 69533), Philips Kornmunika- tions Industrie AG, Nfirnberg, 1988.

[4] CCIR, Future public land mobile telecommunication systems, Report of IWP 13/8 Meeting No. 2, Melbourne, 1987.

[5] B. Eklundh, Channel utilisation and blocking probability in a cellular mobile telephone system with directed retry, 1EEE Trans. Comm. 34 (4) (1986) 329-337.

[6] B. Eklundh and J. Karlsson, Load sharing in a cellular mobile telephone system: Blocking probabilities and channel utilisation, in: Proc. 1SS, Phoenix (1987) 753-758.

[7] D. Everitt and N.W. Macfadyen, Analysis of multicellular mobile radio telephone systems with loss, British Telecom Tech. J. l (2) (1983) 37-45.

[8] D. Everitt and D. Manfield, Performance analysis of cellular mobile communications systems with dynamic


channel assignment, IEEE J. Select. Areas Comm., issue on Telecommunications Networks Design and Planning, 7 (8) (1989) 1172-1180.

[9] B. Ghillebaert, The second generation cellular system, in: Proc. 1SS, Phoenix (1987) 734-738.

[10] J. Karlsson and B. Eklundh, A cellular mobile telephone system with load sharing--An enhancement of directed retry, 1EEE Trans. Comm. 37 (5) (1989) 530-535.

[11] F. Lindell, J. Swerup and J. Uddenfeldt, Digital cellular radio for the 1990's, Telecommunications (October 1987) 254-265.

[12] Y.K. Ling, Alternative routing protocols for cellular mobile radio, in: Proc. 5th UK Teletraffic Symposium, Uni- versity of Aston, UK (1988) 12/1-10.

[13] K. Sallberg, B. Stavenow and B. Eklundh, Hybrid channel assignment and reuse partitioning in a cellular mobile telephone system, in: Proc. 37th IEEE Vehicular Technol- ogy Conference (1987) 405-411.

[14] J.H. S~nchez-Vargas, Traffic performance of cellular mobile radio systems, Ph.D. Thesis, University of Essex, UK, 1988.

[15] J.H. Shnchez-Vargas and J.P. Eade, A simulation study of cellular and sectorised mobile telephone systems using a hybrid channel allocation technique, in: Proc. 5th UK Teletraffic Symposium, University of Aston, UK (1988) 11/1-10.

Traffic capacity of cellular mobile communications systems

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