A single server queue with service interruptions

In this paper we characterize the queue-length distribution as well as the waiting time distribution of a single-server queue which is subject to service interruptions. Such queues arise naturally in computer and communication problems in which customers belong to different classes and share a common server under some complicated service discipline. In such queues, the viewpoint of a given class of customers is that the server is not available for providing service some of the time, because it is busy serving customers from a different class. A natural special case of these queues is the class of preemptive priority queues. In this paper, we consider arrivals according the Markovian Arrival Process (MAP) and the server is not available for service at certain times. The service times are assumed to have a general distribution. We provide numerical examples to show that our methods are computationally feasible.

[1]  M. Neuts,et al.  A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[2]  R. Bellman.  Introduction To Matrix Analysis By Richard Bellman, New York, 1960 , 1960 .

[3]  M. Neuts,et al.  A SINGLE-SERVER QUEUE WITH SERVER VACATIONS AND A CLASS OF NON-RENEWAL ARRIVAL PROCESSES , 1990 .

[4]  W. Whitt,et al.  MULTI-DIMENSIONAL TRANSFORM INVERSION WITH APPLICATIONS TO THE TRANSIENT M / G / 1 QUEUE , 1994 .

[5]  Duan-Shin Lee,et al.  Design and analysis of a congestion-free overlay on a high-speed network , 1997, TNET.

[6]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[7]  Tetsuya Takine,et al.  On the relationship between queue lengths at a random instant and at a departure in the stationary queue with bmap arrivals , 1998 .

[8]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[9]  Ward Whitt,et al.  Numerical Solution of Piecewise-Stationary Mt/Gt/1 Queues , 1997, Oper. Res..

[10]  Tetsuya Takine,et al.  The workload in the MAP/G/1 queue with state-dependent services: its application to a queue with preemptive resume priority , 1994 .

[11]  Richard Bellman,et al.  Introduction to matrix analysis (2nd ed.) , 1997 .

[12]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[13]  Bhaskar Sengupta,et al.  A Queue with Service Interruptions in an Alternating Random Environment , 1990, Oper. Res..

[14]  Awi Federgruen,et al.  Queueing Systems with Service Interruptions , 1986, Oper. Res..

[15]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[16]  Awi Federgruen,et al.  Queueing systems with service interruptions II , 1988 .

[17]  Duan-Shin Lee,et al.  Analysis of a single server queue with semi-Markovian service interruption , 1997, Queueing Syst. Theory Appl..

[18]  Herwig Bruneel,et al.  Analysis of an infinite buffer system with random server interruptions, , 1984, Comput. Oper. Res..

[19]  W. Whitt,et al.  Multidimensional Transform Inversion with Applications to the Transient M/G/1 Queue , 1994 .

[20]  B. Conolly.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1991 .