Queueing Processes

2009 ◽  
pp. 201-225
Author(s):  
Richard M. Feldman ◽  
Ciriaco Valdez-Flores
Keyword(s):  
Queueing Processes

Recent advances in storage and flooding theory

1969 ◽  
Vol 1 (1) ◽  
pp. 90-110 ◽  
Author(s):  
J. Gani
Keyword(s):  
Queueing Theory ◽  
Applied Probability ◽  
The Past ◽  
Continuous Flows ◽  
Recent Advances ◽  
A Minor ◽  
Queueing Processes ◽  
Theory Of Storage ◽  
Storage Processes

The theory of storage processes, originally formulated by Moran [1] in 1954, has developed in the past fourteen years into a minor subfield of Applied Probability, closely allied to queueing theory. While dam models with discrete inputs are analogous to queueing processes, the essentially continuous nature of water inflows has distinguished generalized storage processes from queues. Indeed, some of the most complex of storage problems have arisen in the case of continuous flows.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (01) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

Tail probabilities for non-standard risk and queueing processes with subexponential jumps

1999 ◽  
Vol 31 (2) ◽  
pp. 422-447 ◽  
Author(s):  
Søren Asmussen ◽  
Hanspeter Schmidli ◽  
Volker Schmidt
Keyword(s):  
Renewal Processes ◽  
Tail Probabilities ◽  
Piecewise Constant ◽  
Stationary Increments ◽  
Cox Processes ◽  
Distribution Tail ◽  
Arrival Processes ◽  
Heavy Tailed ◽  
Queueing Processes ◽  
Standard Risk

A well-known result on the distribution tail of the maximum of a random walk with heavy-tailed increments is extended to more general stochastic processes. Results are given in different settings, involving, for example, stationary increments and regeneration. Several examples and counterexamples illustrate that the conditions of the theorems can easily be verified in practice and are in part necessary. The examples include superimposed renewal processes, Markovian arrival processes, semi-Markov input and Cox processes with piecewise constant intensities.

Tail probabilities for non-standard risk and queueing processes with subexponential jumps

1999 ◽  
Vol 31 (02) ◽  
pp. 422-447 ◽  
Author(s):  
Søren Asmussen ◽  
Hanspeter Schmidli ◽  
Volker Schmidt
Keyword(s):  
Renewal Processes ◽  
Tail Probabilities ◽  
Piecewise Constant ◽  
Stationary Increments ◽  
Cox Processes ◽  
Distribution Tail ◽  
Arrival Processes ◽  
Heavy Tailed ◽  
Queueing Processes ◽  
Standard Risk

A well-known result on the distribution tail of the maximum of a random walk with heavy-tailed increments is extended to more general stochastic processes. Results are given in different settings, involving, for example, stationary increments and regeneration. Several examples and counterexamples illustrate that the conditions of the theorems can easily be verified in practice and are in part necessary. The examples include superimposed renewal processes, Markovian arrival processes, semi-Markov input and Cox processes with piecewise constant intensities.

scholarly journals A compensation approach for two-dimensional Markov processes

1993 ◽  
Vol 25 (4) ◽  
pp. 783-817 ◽  
Author(s):  
I. J. B. F. Adan ◽  
J. Wessels ◽  
W. H. M. Zijm
Keyword(s):  
Random Walks ◽  
Markov Processes ◽  
Infinite Series ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Compensation Approach ◽  
Queueing Processes ◽  
Random Behaviour ◽  
Elegant Solution

Several queueing processes may be modeled as random walks on a multidimensional grid. In this paper the equilibrium distribution for the case of a two-dimensional grid is considered. In previous research it has been shown that for some two-dimensional random walks the equilibrium distribution has the form of an infinite series of products of powers which can be constructed with a compensation procedure. The object of the present paper is to investigate under which conditions such an elegant solution exists and may be found with a compensation approach. The conditions can be easily formulated in terms of the random behaviour in the inner area and the drift on the boundaries.

A positive recurrence criterion associated with multidimensional queueing processes

1980 ◽  
Vol 17 (3) ◽  
pp. 790-801 ◽  
Author(s):  
Zvi Rosberg
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Queueing Network ◽  
Multidimensional Case ◽  
Positive Recurrence ◽  
One Dimensional ◽  
Queueing Processes ◽  
Irreducible Markov Chain

A criterion is given for positive recurrence of a multidimensional, aperiodic, irreducible Markov chain with a denumerable state space. This criterion extends to the multidimensional case Foster's one-dimensional criterion. The multidimensional criterion consists of several conditions, one for each coordinate of the process. The usefulness of this criterion is shown through a queueing network example.

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