Abstract
A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided.
Highlights
Queueing theory is very useful for modeling various real-world systems, contact centers, airports, banks, telecommunication, and retail networks, in particular
The cost coefficients a1, b1, b2, d1, and d2 have the following meaning: a1 is the profit obtained by the system for the successful service of one customer; b1 and b2 are the charges paid by the system for the loss of a customer at the entrance of the system and due to impatience, correspondingly; d1 and d2 are the charges paid by the system for maintaining one server and one assistant per unit time, correspondingly; the economic criterion E has the meaning of the average profit obtained by the system per unit of time
We have considered a queueing model having a finite number N of servers and M assistants that help the servers when certain service problems occur
Summary
Queueing theory is very useful for modeling various real-world systems, contact centers, airports, banks, telecommunication, and retail networks, in particular. The model considered in [21] assumes an arbitrary number of servers and assistants (called in this paper, specialist servers); the possibility of providing help by the assistant is only after the main service. This means that the arriving customer can see the number of customers in the queue and can use this information to decide to join a queue or abandon (balk) it, e.g., queueing systems managed by ticket technology is widely used in service industries, as well as government offices, see [23]. In [41,42,43], multi-server queues with the MAP or marked MAP arrival flows and impatient customers as the models of call centers were analyzed via the matrix analytic methods.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
