5,412 research outputs found
An analytic approach to a general class of G/G/s queueing systems
Includes bibliographical references (p. 38-40).by Dimitris Bertsimas
Stochastic analyses arising from a new approach for closed queueing networks
Analyses are addressed for a number of problems in queueing systems and
stochastic modeling that arose due to an investigation into techniques that could
be used to approximate general closed networks.
In Chapter II, a method is presented to calculate the system size distribution at
an arbitrary point in time and at departures for a (n)/G/1/N queue. The analysis
is carried out using an embedded Markov chain approach. An algorithm is also
developed that combines our analysis with the recursive method of Gupta and Rao.
This algorithm compares favorably with that of Gupta and Rao and will solve some
situations when Gupta and Rao's method fails or becomes intractable.
In Chapter III, an approach is developed for generating exact solutions of the
time-dependent conditional joint probability distributions for a phase-type renewal
process. Closed-form expressions are derived when a class of Coxian distributions
are used for the inter-renewal distribution. The class of Coxian distributions was
chosen so that solutions could be obtained for any mean and variance desired in the
inter-renewal times.
In Chapter IV, an algorithm is developed to generate numerical solutions for
the steady-state system size probabilities and waiting time distribution functions of
the SM/PH/1/N queue by using the matrix-analytic method. Closed form results are also obtained for particular situations of the preceding queue. In addition, it
is demonstrated that the SM/PH/1/N model can be implemented to the analysis
of a sequential two-queue system. This is an extension to the work by Neuts and
Chakravarthy.
In Chapter V, principal results developed in the preceding chapters are employed
for approximate analysis of the closed network of queues with arbitrary service
times. Specifically, the (n)/G/1/N queue is applied to closed networks of a
general topology, and a sequential two-queue model consisting of the (n)/G/1/N
and SM/PH/1/N queues is proposed for tandem queueing networks
Lattice path counting and the theory of queues
In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)Series: Research Report Series / Department of Statistics and Mathematic
Power series approximations for two-class generalized processor sharing systems
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation
About a possible analytic approach for walks in the quarter plane with arbitrary big jumps
In this note, we consider random walks in the quarter plane with arbitrary
big jumps. We announce the extension to that class of models of the analytic
approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the
quarter plane, Springer-Verlag, Berlin (1999)], initially valid for walks with
small steps in the quarter plane. New technical challenges arise, most of them
being tackled in the framework of generalized boundary value problems on
compact Riemann surfaces.Comment: 7 pages, 3 figures, extended abstrac
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