AN APPROXIMATION FOR THE QUEUE LENGTH DISTRIBUTION IN A MULTI-SERVER RETRIAL QUEUE

Multi-server queueing systems with retrials are widelyused to model problems in a call center. We present an explicitformula for an approximation of the queue length distribution in amulti-server retrial queue, by using the Lerch transcendent. Accu-racy of our approximation is shown in the numerical examples. 1. IntroductionRetrial queues are queueing systems in which arriving customerswho find all servers occupied may retry for service again after a ran-dom amount of time. Retrial queues have been widely used to modelmany problems/situations in telephone systems, call centers, telecom-munication networks, computer networks and computer systems, and indaily life. For an overview regarding retrial queues, refer to the sur-veys [9, 13, 14]. For further details, refer to the books [7, 10] and thebibliographies [3, 4, 5].Typically a call center consists of a finite number of servers that an-swer customer’s calls, and it can be modelled as a queueing system. In aqueueing model of a call center, the customers are callers and the serversare either telephone operators or communication equipment. Queues areformed by callers who are waiting service. The call center can be de-scribed as follows: When a customer’s call arrives, it will be servedimmediately if a server is available. However, if all servers are busy at