Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/GY/1/M

2010 ◽  
Vol 28 (6) ◽  
pp. 1061-1077
Author(s):  
Mohan L. Chaudhry ◽  
Bong K. Yoon ◽  
Nam K. Kim
Keyword(s):  
Discrete Time ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Single Server ◽  
Finite Capacity ◽  
Single Server Queue ◽  
Server Queue ◽  
Bulk Service

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.

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