Optimization of admission control in tandem queue with heterogeneous customers and pre-service

Abstract

ABSTRACTA new type of tandem queueing systems with heterogeneous customers is analysed. Tandem consists of two stations each of which is modelled by a multi-server queueing system. Type-1 customers need service at station 1. After service at this station, a type-1 customer spends a random amount of time in the so-called pre-service area and then moves for service at station 2. Type-2 customers need service only at station 2 and have lower priority. A strategy of their admission depending on the current number of customers in the pre-service area and station 2 is offered. This strategy is defined by three integers (thresholds). Cost criterion, which defines the quality of the system operation, is the weighted sum of the mean numbers of lost customers from the pre-service area and type-2 customers per unit of time. The most difficult part of solving the problem of minimizing the cost criterion consists of computation of the stationary distribution of the system states under the fixed set of the thresholds. Numerical results are presented. Results can be used for optimization of various real-world systems such as manufacturing, transportation and health-care systems as well as for optimization of booking systems in HORECA (hotel/restaurant/cafe), museums, etc.