Study Group report
This is the final report on the problem of GPRS grade of service, brought to ESGI46 by Motorola Research. It has been prepared by Rob Hinch (University of Oxford) and David Allwright (Smith Institute).

Report authors
Rob Hinch (University of Oxford)
David Allwright (Smith Institute)

Introduction
In this report the GPRS service system for voice and data calls has been modelled as a continuous time Markov chain in various circumstances. When each user has only 1 channel available for data calls, the analysis presented gives ways of calculating the relevant quantities, such as mean service time. These methods are based on the idea of treating the total number of channels N as large and making appropriate approximations, and it is shown that the approximations are good when N = 8, the typical value in practice. Then report also shows how that method can be extended to more complex queues, e.g. where users have more than 1 channel available for data calls. It also deals with the case where all users have N channels available for data calls, and there is dynamic allocation of channels. This can be dealt with analytically by the method of generating functions. Finally the report considers the case where users’ phones can have any number of channels available for data calls, and shows how to set up the transition rate matrix for this. The steady state distribution can then be found computationally, for any distribution of data call capacity in the user population. It is shown how the mean service time for data calls drops as the number of data channels available to users rises. Also the decrease of mean service time for data calls when dynamic channel allocation is used has been shown.

Download 'GPRS.pdf' (255 Kb).