A retrial queue with structured batch arrivals, priorities and server vacations

A retrial queue accepting two types of customers with correlated batch arrivals and preemptive resume priorities is studied. The service times are arbitrarily distributed with a different distribution for each type of customer and the server takes a single vacation each time he becomes free. For such a model the state probabilities are obtained both in a transient and in a steady state. Finally, the virtual waiting time of an arbitrary ordinary customer in a steady state is analysed.

[1]  Brian Conolly,et al.  New results in the theory of repeated orders queueing systems , 1979 .

[2]  P. J. Burke.  Technical Note - Delays in Single-Server Queues with Batch Input , 1975, Oper. Res..

[3]  S. A. Grishechkin.  Multiclass batch arrival retrial queues analyzed as branching processes with immigration , 1992, Queueing Syst. Theory Appl..

[4]  Gennadi Falin,et al.  ON THE VIRTUAL WAITING TIME IN AN M/G/1 RETRIAL QUEUE , 1991 .

[5]  Jesus R. Artalejo,et al.  On the single server retrial queue with priority customers , 1993, Queueing Syst. Theory Appl..

[6]  Gennadi Falin,et al.  On the virtual waiting time for an M/G/1 retrial queue with two types of calls , 1993 .

[7]  Hideaki Takagi,et al.  STRUCTURED PRIORITY QUEUE WITH BATCH ARRIVALS , 1990 .

[8]  Gennadi Falin.  On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls , 1984 .

[9]  Gennadi Falin,et al.  A survey of retrial queues , 1990, Queueing Syst. Theory Appl..

[10]  Bong D. Choi,et al.  The M/G/1 retrial queue with bernoulli schedule , 1990, Queueing Syst. Theory Appl..

[11]  Moshe Sidi,et al.  Structured priority queueing systems with applications to packet-radio networks , 1983, Perform. Evaluation.

[12]  S. A. Grishechkin.  Branching processes and queueing systems with repeated orders or with random discipline , 1991 .

[13]  Erhan Çinlar,et al.  Introduction to stochastic processes , 1974 .

[14]  James G. C. Templeton,et al.  A survey on retrial queues , 1989 .

[15]  V. G. Kulkarni.  Expected waiting times in a multiclass batch arrival retrial queue , 1986 .

[16]  Gennadi Falin.  A single-line system with secondary orders , 1979 .

[17]  G. I. Falin.  On a multiclass batch arrival retrial queue , 1988, Advances in Applied Probability.

[18]  Christos Langaris,et al.  Time-dependent analysis of a queue with batch arrivals andn levels of nonpreemptive priority , 1995, Queueing Syst. Theory Appl..

[19]  Gennadi Falin.  Single-line repeated orders queueing systems 1 , 1986 .

[20]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .