A novel diffusion process with jumps to study an electronic-optical edge router

The article presents a diffusion approximation model applied to investigate the process of filling a large optical packet by smaller and coming irregularly electronic packets. The use of diffusion approximation enables us to include the general distributions of interarrival times, also the self-similarity of the input process, as well as to investigate transient states. We propose a novel diffusion process with jumps representing the end of the filling the buffer due to arrival of too large packet and we give the transient solution to this process. The model allows us to study the distribution of interdeparture times and the distribution of the space occupied in the optical packet

General queueing network models for computer system performance analysis. A maximum entropy method of analysis and aggregation of general queueing network models with application to computer systems.

In this study the maximum entropy formalism [JAYN 57] is suggested as an alternative theory for general queueing systems of computer performance analysis. The motivation is to overcome some of the problems arising in this field and to extend the scope of the results derived in the context of Markovian queueing theory. For the M/G/l model a unique maximum entropy solution., satisfying locALl balance is derived independent of any assumptions about the service time distribution. However, it is shown that this solution is identical to the steady state solution of the underlying Marko-v process when the service time distribution is of the generalised exponential (CE) type. (The GE-type distribution is a mixture of an exponential term and a unit impulse function at the origin). For the G/M/1 the maximum entropy solution is identical in form to that of the underlying Markov process, but a GE-type distribution still produces the maximum overall similar distributions. For the GIG11 model there are three main achievements: first, the spectral methods are extended to give exaft formulae for the average number of customers in the system for any G/G/l with rational Laplace transform. Previously, these results are obtainable only through simulation and approximation methods. (ii) secondly, a maximum entropy model is developed and used to obtain unique solutions for some types of the G/G/l. It is also discussed how these solutions can be related to the corresponding stochastic processes. (iii) the importance of the G/GE/l and the GE/GE/l for the analysis of general networks is discussed and some flow processes for these systems are characterised. For general queueing networks it is shown that the maximum entropy solution is a product of the maximum entropy solutions of the individual nodes. Accordingly, existing computational algorithms are extended to cover general networks with FCFS disciplines. Some implementations are suggested and a flow algorithm is derived. Finally, these results are iised to improve existing aggregation methods. In addition, the study includes a number of examples, comparisons, surveys, useful comments and conclusions

General queueing networks with priorities. Maximum entropy analysis of general queueing network models with priority preemptive resume or head-of-line and non-priority based service disciplines.

Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made.Algerian governmen