TheM/G/1 retrial queue with the server subject to starting failures

In this paper, we study a retrial queueing model with the server subject to starting failures. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system in steady state. We show that the general stochastic decomposition law forM/G/1 vacation models also holds for the present system. Finally, we demonstrate that a few well known queueing models are special cases of the present model and discuss various interpretations of the stochastic decomposition law when applied to each of these special cases.

[1]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[2]  Yang Woo Shin,et al.  Retrial queues with collision arising from unslottedCSMA/CD protocol , 1992, Queueing Syst. Theory Appl..

[3]  Do Le Minh,et al.  Analysis of the Exceptional Queueing System by the Use of Regenerative Processes and Analytical Methods , 1980, Mathematics of Operations Research.

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

[5]  Peter D. Welch,et al.  On a Generalized M/G/1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service , 1964 .

[6]  Robert B. Cooper.  Queues served in cyclic order: Waiting times , 1970, Bell Syst. Tech. J..

[7]  Vidyadhar G. Kulkarni,et al.  Retrial queues with server subject to breakdowns and repairs , 1990, Queueing Syst. Theory Appl..

[8]  Austin J. Lemoine,et al.  Limit Theorems for Generalized Single Server Queues: The Exceptional System , 1975 .

[9]  P. Burke.  Proof of a Conjecture on the Interarrival-Time Distribution in an M/M/1 Queue with Feedback , 1976, IEEE Trans. Commun..

[10]  A. G. Pakes,et al.  Some Conditions for Ergodicity and Recurrence of Markov Chains , 1969, Oper. Res..

[11]  Leonard Kleinrock,et al.  On the M/G/1 Queue with Rest Periods and Certain Service-Independent Queueing Disciplines , 1983, Oper. Res..

[12]  Marcel F. Neuts,et al.  A service model in which the server is required to search for customers , 1984 .

[13]  T. T. Soong,et al.  Book Reviews : INTRODUCTION TO STOCHASTIC PROCESSES E. Cinlar Prentice-Hall, 1975 , 1979 .

[14]  Bharat T. Doshi,et al.  A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times , 1985, Journal of Applied Probability.

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

[16]  Julian Keilson,et al.  A Service System with Unfilled Requests Repeated , 1968, Oper. Res..

[17]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

[18]  Daniel P. Heyman,et al.  Optimal Operating Policies for M/G/1 Queuing Systems , 1968, Oper. Res..

[19]  Austin J. Lemoine,et al.  Limit theorems for generalized single server queues , 1974, Advances in Applied Probability.

[20]  Leonard Kleinrock,et al.  Time-shared Systems: a theoretical treatment , 1967, JACM.

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

[22]  S. W. Fuhrmann.  Technical Note - A Note on the M/G/1 Queue with Server Vacations , 1984, Oper. Res..

[23]  Leonard Kleinrock,et al.  Analysis of A time‐shared processor , 1964 .

[24]  Leonard Kleinrock,et al.  A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition , 1986, Oper. Res..

[25]  U. Yechiali,et al.  Utilization of idle time in an M/G/1 queueing system Management Science 22 , 1975 .

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