Abstract
The use of priorities allows us to improve the quality of service of inhomogeneous customers in telecommunication networks, inventory and health-care systems. An important modern direction of research is to analyze systems in which priority of a customer can be changed during his/her stay in the system. We considered a single-server queuing system with a finite buffer, where two types of customers arrive according to a batch marked Markov arrival process. Type 1 customers have non-preemptive priority over type 2 customers. Low priority customers are able to receive high priority after the random amount of time. For each non-priority customer accepted into the buffer, a timer, which counts a random time having a phase type distribution, is switched-on. When the timer expires, the customer with some probability leaves the system unserved and with the complimentary probability gains the high priority. Such a type of queues is typical in many health-care systems, contact centers, perishable inventory, etc. We describe the behavior of the system by a multi-dimensional continuous-time Markov chain and calculate a number of the stationary performance measures of the system including the various loss probabilities as well as the distribution function of the waiting time of priority customers. The illustrative numerical examples giving insights into the system behavior are presented.
Highlights
Queuing theory is very useful for solving the problems of optimal sharing and scheduling restricted resources in many real world systems
The model considered in this paper can be used for description of operation of a contact center. As it is mentioned in the literature, phone calls have high priority, and requests sent by e-mail or a messenger have low priority; the customer who used a messenger for receiving information can make a phone call if his/her waiting for a response is too long
In order to investigate the behavior of L( prior) and L for BMMAP3 in more detail, we examine the deviations of the number of priority customers and the total number of customers in the buffer from their average values
Summary
Queuing theory is very useful for solving the problems of optimal sharing and scheduling restricted resources in many real world systems. The model considered in this paper can be used for description of operation of a contact center As it is mentioned in the literature, phone calls have high priority, and requests sent by e-mail or a messenger have low priority; the customer who used a messenger for receiving information can make a phone call if his/her waiting for a response is too long.
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