Stochastic scheduling of parallel queues with set-up costs

We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a set-up cost. The objective is to minimize the expected cost due to the waiting of jobs and the switching of the server. A set-up cost is required to effect an instantaneous switch from one queue to another. We partially characterize an optimal policy and provide a simple heuristic scheduling policy. The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances with four queues.

[1]  Kevin Mahon,et al.  Deterministic and Stochastic Scheduling , 1983 .

[2]  Donald F. Towsley,et al.  On optimal polling policies , 1992, Queueing Syst. Theory Appl..

[3]  Isaac Meilijson,et al.  On optimal right-of-way policies at a single-server station when insertion of idle times is permitted , 1977 .

[4]  Jean Walrand,et al.  The c# rule revisited , 1985 .

[5]  Van Oyen,et al.  Optimal stochastic scheduling of queueing networks: Switching costs and partial information. , 1992 .

[6]  G. Klimov.  Time-Sharing Service Systems. I , 1975 .

[7]  Moshe Sidi,et al.  Dominance relations in polling systems , 1990, Queueing Syst. Theory Appl..

[8]  Armand M. Makowski,et al.  K competing queues with geometric service requirements and linear costs: The μc-rule is always optimal☆ , 1985 .

[9]  T. Lai,et al.  Open bandit processes and optimal scheduling of queueing networks , 1988, Advances in Applied Probability.

[10]  Ger Koole,et al.  Asigning a Single Server to Inhomogeneous Queues with Switching Costs , 1997, Theor. Comput. Sci..

[11]  J. Walrand,et al.  Interchange arguments in stochastic scheduling , 1989 .

[12]  Jean Walrand,et al.  Extensions of the multiarmed bandit problem: The discounted case , 1985 .

[13]  J. Michael Harrison,et al.  A Priority Queue with Discounted Linear Costs , 1975, Oper. Res..

[14]  Hideaki Takagi,et al.  Priority Queues with Setup Times , 1990, Oper. Res..

[15]  Micha Hofri,et al.  On the Optimal Control of Two Queues with Server Setup Times and its Analysis , 1987, SIAM J. Comput..

[16]  J. Bather,et al.  Multi‐Armed Bandit Allocation Indices , 1990 .

[17]  E. J. Collins,et al.  THE JOB SEARCH PROBLEM AS AN EMPLOYER-CANDIDATE GAME , 1990 .

[18]  D. Teneketzis,et al.  Optimal stochastic scheduling of forest networks with switching penalties , 1994, Advances in Applied Probability.

[19]  Christian M. Ernst,et al.  Multi-armed Bandit Allocation Indices , 1989 .

[20]  Guy Pujolle,et al.  Introduction to queueing networks , 1987 .

[21]  J. Walrand,et al.  The cμ rule revisited , 1985, Advances in Applied Probability.

[22]  P. Nain,et al.  Interchange arguments for classical scheduling problems in queues , 1989 .

[23]  Izak Duenyas,et al.  Heuristic Scheduling of Parallel Heterogeneous Queues with Set-Ups , 1996 .

[24]  J. Michael Harrison,et al.  Dynamic Scheduling of a Multiclass Queue: Discount Optimality , 1975, Oper. Res..

[25]  G. P. Klimov.  Time sharing service systems ii , 1978 .

[26]  Moshe Sidi,et al.  Polling systems: applications, modeling, and optimization , 1990, IEEE Trans. Commun..

[27]  Hanoch Levy,et al.  Efficient visit frequencies for polling tables: minimization of waiting cost , 1991, Queueing Syst. Theory Appl..

[28]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[29]  D. Teneketzis,et al.  Optimality of index policies for stochastic scheduling with switching penalties , 1992, Journal of Applied Probability.