Randomly Timed Gated Queueing Systems

Timers are used as a control mechanism to constrain the service periods in various telecommunication networks. In this paper we introduce and analyze a general family of timer-type models, called Randomly Timed Gated (RTG) queueing systems, which, in addition, extends and generalizes the family of M/G/1-type queues with server intermissions. The control mechanism is such that, whenever the server reenters the system, an exponential Timer T is activated. If the server empties the queue before the Timer's expiration, it immediately leaves for another intermission. Otherwise (if the Timer expires when there is still work in the system), the server obeys one of the following rules, each leading to a different model: (1) The server completes all the work accumulated up to time T, and leaves. (2) The server completes only the service of the job currently being served, and leaves. (3) The server leaves immediately. Consequently, the RTG queue forms a unified structure for a vast collection of timer-type models: ...

[1]  Edward G. Coffman,et al.  Two Queues with Alternating Service Periods , 1987, Performance.

[2]  Kin K. Leung,et al.  A single-server queue with vacations and gated time-limited service , 1990, IEEE Trans. Commun..

[3]  Eitan Altman.  Analysing Timed-Token Ring Protocols Using the Power Series Algorithm 1 , 1994 .

[4]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

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

[6]  Kin K. Leung,et al.  A Single-Server Queue with Vacations and Non-Gated Time-Limited Service , 1991, Perform. Evaluation.

[7]  Kin K. Leung,et al.  Two Vacation Models for Token-Ring Networks where Service is Controlled by Timers , 1994, Perform. Evaluation.

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

[9]  Daniel P. Heyman,et al.  Stochastic models in operations research , 1982 .

[10]  Christine Fricker,et al.  Monotonicity and stability of periodic polling models , 1994, Queueing Syst. Theory Appl..

[11]  Robert B. Cooper,et al.  An Introduction To Queueing Theory , 2016 .

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

[13]  Offer Kella,et al.  Priorities in M/G/1 queue with server vacations , 1988 .

[14]  Sem C. Borst,et al.  Polling systems with multiple coupled servers , 1995, Queueing Syst. Theory Appl..

[15]  Kin K. Leung.  Cyclic-service systems with nonpreemptive, time-limited service , 1994, IEEE Trans. Commun..

[16]  Uri Yechiali.  Analysis and Control of Poling Systems , 1993, Performance/SIGMETRICS Tutorials.