Slow Retrial Asymptotics for a Single Server Queue with Two-Way Communication and Markov Modulated Poisson Input

2019 ◽  
Vol 28 (2) ◽  
pp. 181-193 ◽  
Author(s):  
Anatoly Nazarov ◽  
Tuan Phung-Duc ◽  
Svetlana Paul
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Markov Modulated

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (4) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

A single-server queue with server vacations and a class of non-renewal arrival processes

1990 ◽  
Vol 22 (3) ◽  
pp. 676-705 ◽  
Author(s):  
David M. Lucantoni ◽  
Kathleen S. Meier-Hellstern ◽  
Marcel F. Neuts
Keyword(s):  
Waiting Times ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Arbitrary Time ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Server Queue ◽  
Arrival Processes ◽  
Markov Modulated

We study a single-server queue in which the server takes a vacation whenever the system becomes empty. The service and vacation times and the arrival process are all assumed to be mutually independent. The successive service times and the vacation times each form independent, identically distributed sequences with general distributions. A new class of non-renewal arrival processes is introduced. As special cases, it includes the Markov-modulated Poisson process and the superposition of phase-type renewal processes.Algorithmically tractable equations for the distributions of the waiting times at an arbitrary time and at arrivals, as well as for the queue length at an arbitrary time, at arrivals, and at departures are established. Some factorizations, which are known for the case of renewal input, are generalized to this new framework and new factorizations are obtained. The algorithmic implementation of these results is discussed.

Waiting time and workload in queues with periodic Poisson input

1989 ◽  
Vol 26 (02) ◽  
pp. 390-397 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Differential Equation ◽  
Waiting Time ◽  
Arrival Rate ◽  
Time Of Day ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Service Distribution ◽  
Server Queue ◽  
General Service

This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (04) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i . The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i . In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

The single server queue with Poisson input and semi-Markov service times

1966 ◽  
Vol 3 (1) ◽  
pp. 202-230 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Markov Process ◽  
Time Dependence ◽  
Stationary Solutions ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Semi Markov Process ◽  
Poisson Arrivals ◽  
Service Times

We assume that the successive service times in a single server queue with Poisson arrivals form an m-state semi-Markov process.The results for the M/G/1 queue are extended to this case. Both the time-dependence and the stationary solutions are discussed.

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