Poission process and related processes renewal-reward processes discrete-time Markov chains continuous-time Markov chains Markov chains and queues discrete-time Markov decision processes semi-Markov decision processes advanced renewal theory algorithms analysis of queuing models useful tools in applied probability useful probability distributions generating functions the discrete fast Fourier transform Laplace transformtheory numerical Laplace inversion the root-finding problem.

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A First Course in Stochastic Models

The traffic analysis of small-cell mobile networks with dynamic channel assignment is investigated to determine their blocking performance, using a hybrid method of analysis and simulation. The authors particularly focus on the performance problems presented by networks with heterogeneous cell traffic loads, the impact of traffic volatility among the cells, and the impact of multichannel traffic on the channel blocking probabilities. Significant improvement in network performance with dynamic channel assignment is established by numerical results. >

Performance analysis of cellular mobile communication systems with dynamic channel assignment

A directed retry facility, which enables subscribers in a mobile telephone system to look for free radio channels in more than one cell, is investigated with respect to blocking probability and channel utilization. An iterative procedure is devised, by which the dependencies among cells can be illustrated. This procedure makes use of theories developed for overflow systems in classical telephony, and proves to be very accurate for the situations under study. Analytical results are compared with simulations and good agreement is observed. Results show that a substantial improvement, compared with systems without a directed retry facility, can be achieved as far as carried traffic is concerned. The improvement is accomplished at the expense of those subscribers who cannot make use of the directed retry facility due to variations in radio coverage.

Channel Utilization and Blocking Probability in a Cellular Mobile Telephone System with Directed Retry

This paper investigates the channel holding time and call inter-arrival distributions in cellular telephony systems. Up until now, it has been generally assumed that both these distributions can be approximated by the negative exponential model. A study is presented which, using real cellular data, determines the actual distributions. It is shown that the negative exponential assumption for channel holding time is not correct and that a lognormal model approximation fits much closer.

Probability distribution of channel holding time in cellular telephony systems

Numerical techniques for modeling computer networks under nonstationary conditions are discussed, and two distinct approaches are presented. The first approach uses a queuing theory formulation to develop differential equation models which describe the behavior of the network by time-varying probability distributions. In the second approach, a nonlinear differential equation model is developed for representing the dynamics of the network in terms of time-varying mean quantities. This approach allows multiple classes of traffic to be modeled and establishes a framework for the use of optimal control techniques in the design of network control strategies. Numerical techniques for determining the queue behavior as a function of time for both approaches are discussed and their computational advantages are contrasted with simulation. >

Numerical methods for modeling computer networks under nonstationary conditions

Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline The first method is based on the use of the fast Fourier transform (FFT) for producing iterative solutions to a discrete version of Lindley's integral equation for both nonsteady state and equilibrium conditions The second method makes use of the complex cepstrum, implemented with the FFT, for providing direct solutions with the queue in equilibrium

Computing the Waiting Time Distribution for the G/G/1 Queue by Signal Processing Methods

A method for increasing the traffic capacity of connecting networks is presented which involves rearrangement of calls while in progress. In contrast to previously studied methods for rearrangement of existing calls, the process involves repacking calls as existing calls terminate, rather than when arriving calls are blocked. The scheme has the advantage that the added control complexity is much less than required for rearrangement in the normal sense.

Call Repacking in Connecting Networks

New teletraffic formulas are derived for the congestion in multicell mobile radio telephone systems. Fixed, dynamic, and hybrid channel asignment are considered and "tromboning," where mobileto-mobile calls go via a base station, is taken into account. The formulas agree with previously published sumulation results.

Teletraffic Analysis for Multicell Mobile Radio Telephone Systems

Formulas are derived for the congestion in single-cell mobile radio systems in which there are both land-to-mobile and mobile-to-mobile calls and in which mobile-to-mobile calls go via the base station. Two approaches are used. The first yields modified forms of the familiar Erlang and Engset formulas. The second gives more complicated but more accurate formulas. The results of computer simulations to establish the accuracy of the formulas are described.

Teletraffic Analysis for Single-Cell Mobile Radio Telephone Systems

A procedure is given for the computation of the transient state occupancy probabilities of the M/M/1 queue. The method makes use of the inverse discrete Fourier transform, computed by means of the fast Fourier transform. It avoids the direct evaluation of modified Bessel functions and sidesteps difficulties due to the computation of very large and very small intermediate quantities.

M. Ackroyd

Papers

Computing the Waiting Time Distribution for the G/G/1 Queue by Signal Processing Methods

Call Repacking in Connecting Networks

Teletraffic Analysis for Multicell Mobile Radio Telephone Systems

Teletraffic Analysis for Single-Cell Mobile Radio Telephone Systems

M/M/1 Transient State Occupancy Probabilities Via the Discrete Fourier Transform