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Paper details
Number 2 - June 2017
Volume 27 - 2017
A queueing system with heterogeneous impatient customers and consumable additional items
Janghyun Baek, Olga Dudina, Chesoong Kim
Abstract
A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered.
Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers
and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products,
half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number
of consumable additional items depending on the type of the customer. The service time has a phase-type distribution
depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service
after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and
maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service
of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds
the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of
optimization problems.
Keywords
marked Markovian arrival process, consumable additional items, phase-type distribution, impatient customers