Optimal control of a system with two servers and two customer classes under a flexible server

Abstract

Many organizations such as manufacturing companies, banks, hospitals, airlines, restaurants, telecmnmunication companies use queuing systems to allocate resources in order to manage de1nand effectively. Besides the efficiency, industries use queuing systen1s also to provide a high level of service quality. Industries use different types of queuing systems according to t heir needs. We consider a queuing system that can be used at branches of banks. At a branch, there is always arrival of customers needed to serve at different service points upon their transaction. Managing branches requires use of resources effectively. This leads to obtain flexible staff in order to manage trade off between service quality and efficiency. In general, flexible server is the person doing both back office and front office activities while dedicated server (teller) is just respon sible of doing the front office activities. We consider a dynan1ic scheduling of a queuing syste1n with two servers where one of t he server is dedicated and the other server is flexible. There are also two types of customers arriving to the system. Server one is dedicated to give service to type-1 customer, while server two is flexible to give service to both types of custmners. Customers arrive to the system according to a poisson process and service rates are exponentially distributed. The syste1n consists of waiting and abandonment costs of customers. We try to optimize the syste1n by Ininiinizing the cost w bile assigning the servers to the customers in the system. In the optimal solut ion of the problem we observe different types of outputs from dyna1nic scheduling model which are mainly names as static, linear switching and threshold models. Sam ples from the experiment that reflect these patterns are shown. In addition, we also construct some heuristics and compare the results with opti1nal policy.