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Modelling communication networks, present and future
 THE CLIFFORD PATTERSON LECTURE
, 1995
"... Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The ..."
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Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.
Dynamic Routing in Stochastic Networks
, 1995
"... . This paper reviews some current work on routing in loss and queueing networks. We describe two classes of bound on the performance of any dynamic routing scheme, together with some open questions concerning whether the bounds can be approached under certain limiting regimes. The first class of bou ..."
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. This paper reviews some current work on routing in loss and queueing networks. We describe two classes of bound on the performance of any dynamic routing scheme, together with some open questions concerning whether the bounds can be approached under certain limiting regimes. The first class of bound is particularly appropriate for networks in heavy traffic, where the key feature of a good routing scheme is its effective utilization of various pooled resources identified by a fluid version of the routing problem. The second class of bound is particularly appropriate for highly connected networks, with many alternative paths. Again, a network flow representation is central, but this time involving a collection of Markov decision processes, one for each resource of the network. Despite their simplicity, the bounds are able to identify the great variety of qualitatively distinct behaviour expected of a good dynamic routing scheme, depending on a network's size, connectivity, asymmetry an...
Blocking Probability Estimates in a Partitioned Sector TDMA System
"... We consider a Time Division Multiple Access (TDMA) system in which each sector is allocated a fixed set of frequency bands. Due to spatial variation in the nature of interference, a voice call originating in a sector may have an acceptable signal to noise ratio only on a subset of the sector's ..."
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We consider a Time Division Multiple Access (TDMA) system in which each sector is allocated a fixed set of frequency bands. Due to spatial variation in the nature of interference, a voice call originating in a sector may have an acceptable signal to noise ratio only on a subset of the sector's frequencies. Given a Poisson traffic arrival distribution, we derive estimates of the sector blocking probability. In particular, we present lower bounds that are independent of the specific call allocation algorithm, and also examine specific call assignment algorithms such as Repacking, Least Busy and Optimal Random Routing. We develop a simple heuristic that allows us to obtain fast and accurate sector blocking probability estimates. The latter serve as crucial inputs for the design and optimization of capacity and coverage in TDMA networks. 1. INTRODUCTION One crucial problem in a TDMA (time division multiple access) system, such as the North American IS136 system or the European GSM (Glob...