Abstract
A multi-server queueing system with a Markovian Arrival Process (MAP), an infinite buffer and impatient customers useful in modeling a call center with a call-back option is investigated. The service time of a customer by a server has an exponential distribution. If all servers are busy at a customer arrival epoch, the customer may leave the system forever or move to the buffer (such a customer is referred to as a real customer), or, alternatively, request for call-back (such a customer is referred to as a virtual customer). During a waiting period, the real customer can be impatient and can leave the system without the service or request for call-back (becomes a virtual customer). An efficient algorithm for calculating the stationary probabilities of system states is proposed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution for virtual customers is derived. Some numerical results are presented.
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Kim, C., Dudina, O., Dudin, A., Dudin, S. (2012). Queueing System MAP/M/N as a Model of Call Center with Call-Back Option. In: Al-Begain, K., Fiems, D., Vincent, JM. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2012. Lecture Notes in Computer Science, vol 7314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30782-9_1
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DOI: https://doi.org/10.1007/978-3-642-30782-9_1
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