Abstract
In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics.
Highlights
The very rapidly spreading and upgrading of telecommunications and computer technology has led to combination and simultaneous maintenance of inter-generational systems
Such systems often face the challenge of optimal routing between parallel queues which can be either dynamic or static
We provide the model to calculate the optimal open-loop routing policy and corresponding optimal allocation policies for the servers in two heterogeneous queues operating in parallel
Summary
The very rapidly spreading and upgrading of telecommunications and computer technology has led to combination and simultaneous maintenance of inter-generational systems. A classical routing problem in exponential system with K parallel heterogeneous servers was studied in [6] with respect to the SQ policy which, in general, eliminate the service rates and cost structure and to the shortest expected delay (SED) routing which takes these attributes into account. Systems where each of the parallel queues is supplied with a multi-server service area were considered in [7], where a static policy in form of the optimal Bernoulli splitting, and three alternative dynamic index policies were considered. The main aim of the paper is to study the open-loop control problem with an application to parallel queues, each of them has two heterogeneous servers operating at different service rates.
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