A method for determining the upper and lower bounds for performance measures for certain types of Generalised Semi-Markov Processes has been described in Taylor and Coyle [8]. A brief description of this method and its use in finding an upper bound for the time congestion of a GI/M/n/n queueing system will be given. This bound turns out to have a simple form which is quickly calculated and easy to use in practice.

This paper describes a mathematical model for a broadband integrated services network offered traffic of many different types. Performance measures are introduced related to revenue generation and overall grade-of-service, providing criteria for the optimal management of resources. Simple asymptotic expressions are derived for quantities termed the “implied costs”, which measure the effect on performance of changes in parameters that are controllable by network management, or that are subject to variation. These implied costs may be used, both to implement optimal bandwidth allocation polices, and also to indicate which services may share a single facility without adversely affecting performance, and which might require a dedicated facility. Asymptotic results are also used to examine how to make efficient use of capacity that is shared between calls with fluctuating bit-rate requirements.

Stochastic Petri Nets are used extensively to find performance measures for communication protocols. This paper illustrates how equilibrium distributions for the markings of a wide class of nets can be found directly without the need to generate a large state space and then resort to equilibrium balance equations.

In the paper we study the conditions under which multiconnection networks are nonblocking. A multiconnection network deals with the connections of pairs {(T1, T2)} where T1 is a subset of the input terminals and T2 is a subset of the output terminals. We investigate networks composed of digital switching matrices. Such networks can be treated as a very general case encompassing many kinds of networks used in practice as well as studied theoretically.

We present four routing strategies and then develop conditions under which multiconnection networks are nonblocking when each of these strategies is used. We also show that the obtained conditions reduce to known results for some values of network parameters.

In this paper we review a simple class of fixed point models for loss networks. We illustrate how these models can readily deal with heterogeneous call types and with simple dynamic routing strategies, and we outline some of the recent mathematical advances in the study of such models. We describe how fixed point models lead to a natural and tractable definition of the implied cost of carrying a call, and how this concept is related to issues of routing and capacity expansion in loss networks.

We consider a hybrid switch which provides integrated packet (asynchronous) and circuit (isochronous) switching. Queue size and delay distribution of the packet switched traffic in the steady state are derived by modelling the packet queue as a queue in a Markovian environment. The arrival process of the packets as well as of the circuit allocation requests are both modelled by a Poisson process. The analysis is performed for several circuit allocation policies, namely repacking, first-fit (involving static or dynamic renumbering) and best-fit. Both exact results and approximations are discussed. Numerical results are presented to demonstrate the effect of increase in packet and circuit loading on the packet delay for each of the policies.