On a queueing model with service interruptions

htmlabstractSingle-server queues in which the server takes vacations arise naturally as models for a wide range of computer-, communication- and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload and queue length processes. In the present study we allow the length of a vacation to depend on the length of the previous active period, viz., the period since the previous vacation. Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution. We conclude by discussing several special cases including polling models, and relate our findings to results obtained earlier.

[1]  Onno J. Boxma,et al.  Workloads and waiting times in single-server systems with multiple customer classes , 1989, Queueing Syst. Theory Appl..

[2]  J. George Shanthikumar.  On Stochastic Decomposition in M/G/1 Type Queues with Generalized Server Vacations , 1988, Oper. Res..

[3]  N. U. Prabhu,et al.  Stochastic Storage Processes , 1980 .

[4]  Iddo Eliazar.  Gated Polling Systems with Lévy Inflow and Inter-Dependent Switchover Times: A Dynamical-Systems Approach , 2005, Queueing Syst. Theory Appl..

[5]  Offer Kella,et al.  An exhaustive lĕvy storage process with intermittent output , 1998 .

[6]  Upendra Dave,et al.  Applied Probability and Queues , 1987 .

[7]  Lajos Takács.  Two Queues Attended by a Single Server , 1968, Oper. Res..

[8]  Eitan Altman,et al.  Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

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

[10]  Eitan Altman.  Stochastic Recursive Equations with Applications to Queues with Dependent Vacations , 2002, Ann. Oper. Res..

[11]  William G. Marchal,et al.  State Dependence in M/G/1 Server-Vacation Models , 1988, Oper. Res..

[12]  Bharat T. Doshi.  Conditional and unconditional distributions forM/G/1 type queues with server vacations , 1990, Queueing Syst. Theory Appl..

[13]  Onno Boxma,et al.  Pseudo-conservation laws in cyclic-service systems , 1986 .

[14]  Hideaki Takagi,et al.  Queueing analysis of polling models: progress in 1990-1994 , 1998 .

[15]  Jacques Teghem,et al.  Control of the service process in a queueing system , 1986 .

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

[17]  D. Bharat.  Generalizations of the stochastic decomposition results for single server queues with vacations , 1990 .