Single server queuing models

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications

This paper discusses the analysis of a single server finite queue with Poisson arrival and arbitrary service time distribution, wherein the arrival rates are state dependent which are all distinct or all equal, service times are conditioned on the system length at the moment of service initiation. The analytic analysis of the queue is carried out and the final results have been presented in the form of recursive equations which can be easily programmed on any PC to obtain the distributions of number of customers in the system at arbitrary, departure and pre-arrival epochs. It is shown that the method works for all service time distributions including the non-phase type and also for low and high values of the model parameters. Some performance measures, and relations among the state probabilities at arbitrary, departure and pre-arrival epochs are also discussed. Furthermore, it is shown that results for a number of queueing models can be obtained from this model as special cases.

This example shows how to model a single-queue single-server system that has a Poisson arrival process and a server with constant service time. The queue has an infinite storage capacity. Entity Generator block: Models a Poisson arrival process by generating entities also known as "customers" in queuing theory. Simulink Function exponentialArrivalTime : Returns data representing the interarrival times for the generated entities.

hochzeitsspiele kennenlernen

The 31 papers presented in this volume were carefully reviewed and selected from 85 submissions. The conference covers various aspects of mathematical modeling and information technologies, focusing on probabilistic methods and models, queueing theory and communication networks. A single server retrial queueing model, in which customers arrive according to a batch Markovian arrival process BMAP , is considered. An arriving batch, finding server busy, enters an orbit. Otherwise one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit try to reach the server subsequently and the inter-retrial times are exponentially distributed.

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Single server queuing simulation

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