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Full-Text Articles in Mathematics
A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj
A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj
Mathematics and System Engineering Faculty Publications
This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size. The objective of the paper is …
On A Single-Server Queue With Fixed Accumulation Level, State Dependent Service, And Semi-Markov Modulated Input Flow, Gary Russell, Jewgeni H. Dshalalow
On A Single-Server Queue With Fixed Accumulation Level, State Dependent Service, And Semi-Markov Modulated Input Flow, Gary Russell, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity is r≥1 and that any service act will not begin until the queue accumulates at least r units. In this model, therefore, idle periods also depend upon the queue length. The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity …
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …
On Solvability Of Mixed Monotone Operator Equations With Applications To Mixed Quasimonotone Differential Systems Involving Discontinuities, Seppo V. Heikkilä, Martti Kumpulainen, V. Lakshmikantham
On Solvability Of Mixed Monotone Operator Equations With Applications To Mixed Quasimonotone Differential Systems Involving Discontinuities, Seppo V. Heikkilä, Martti Kumpulainen, V. Lakshmikantham
Mathematics and System Engineering Faculty Publications
In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence of coupled extremal quasisolutions of the systems of first and second order mixed quasimonotone differential equations with discontinuous right hand sides. Most of the results deal with systems in a Banach space ordered by a regular order cone.