Strongly asymptotically optimal design and control of production and service systems

Abstract

In this paper we consider production and service systems that can be modeled as single or multiple stage queueing networks. We provide a formal definition of strong asymptotic optirnality in the context of design and control of such queueing systems. We describe a simple approach to obtain strongly asymptotically optimal design and control policies for these systems. We illustrate our approach through some examples. In particular we obtain a strongly asymptotically optimal workload allocation for a multiple center service system modeled by the open Jackson network. The objective here is to minimize the expected total holding cost. A simple counter example shows that the much celebrated balanced workload allocation is not even asymptotjcally optimal for minimizing the expected number of jobs in the system. We show that an index policy is strongly asymptotically optimal for the scheduling control problem in a single stage (GIGIIl) service system. We also obtain a strongly asymptotically optimal allocation of classes of customers to a multiple center service system. This allocation agrees with the traditional wisdom of forming service stations to process similar tasks that reduce fluctuations in processing times. Suggestions for further work on this topic are summarized as well.

Análise de problemas de partição de instalações em sistemas job-shops por meio de modelos de redes de filas

“…Estes problemas já foram objeto de diversos estudos anteriores em sistemas job-shops, por exemplo, em Bitran & Tirupati (1989), Boxma et al (1990), Van Vliet & Rinnooy Kan (1991), Bitran & Sarkar (1994a), Bitran & Morabito (1995, 1996 e Silva & Morabito (2007). Outros estudos relacionados aparecem em Calabrese (1992), Frenk et al (1994), Sundarraj et al (1994), Bretthauer (1996), Seshadri & Pinedo (1999), Shanthikumar & Xu (2000), …”

Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload

“…Equations (13)- (15) (18) describe the evolution of class 1 fluid level from s 2 to t 2 under the policy that gives higher priority to class 1. Equation (16) implies that at time t 1 , class 1 fluid level increases to its threshold θ 1 . Equation (17) records the class 1 fluid level at the end of the high period.…”

“…In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal in the following sense: the difference between its performance and the optimality is bounded from above by a constant even as the optimal value itself goes to infinity. This notion of strong asymptotic optimality has also been considered in [16,19], as a measure to evaluate the closeness to optimality of approximating control policies. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.…”