Abstract
This paper considers optimal admission and routing control in multi-class service systems in which customers can either receive quality regular service which is subject to congestion or can receive congestion-free but less desirable service at an alternative service station, which we call the self-service station. We formulate the problem within the Markov decision process framework and focus on characterizing the structure of dynamic optimal policies which maximize the expected long-run rewards. For this, value function and sample path arguments are used. The congestion sensitivity of customers is modeled with class-independent holding costs at the regular service station. The results show how the admission rewards of customer classes affect their priorities at the regular and self-service stations. We explore that the priority for regular service may not only depend on regular service admission rewards of classes but also on the difference between regular and self-service admission rewards. We show that optimal policies have monotonicity properties, regarding the optimal decisions of individual customer classes such that they divide the state space into three connected regions per class.
Highlights
This paper focuses on the challenge of service providers to cope with dynamic and varying customer demands with their limited resources
The so-called trunks reserved per customer class depend on the admission rewards; if customer class i offers reward ri which is greater than rj, the admission reward that class j offers, at any congestion level that class j is accepted, for sure class i must be admitted to the system
This paper focuses on the optimal dynamic admission and routing control problem for the revenue management in a specific service system setting
Summary
This paper focuses on the challenge of service providers to cope with dynamic and varying customer demands with their limited resources. The admission control studies which consider class-dependent service rates have focused on providing heuristic policies. Kocaga and Ward [16] considered congestion-related costs through the abandonment of customers in their single-class multi-server model for controlling the admission decisions of arriving customers. Feinberg and Yang [10] considered congestion effects through class-dependent holding costs in the admission control problem of a multi-class queue model. For systems with many service stations and/or customer classes, the use of asymptotic analysis is common in the literature to provide efficient routing policies. Atar et al [3] studied the routing control problem in the diffusion models of multi-class many-server queueing systems. For single-class systems with parallel servers with holding costs, there are many results on the optimal dynamic routing policies in the literature.
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