Discrete-Time Models for Communication Systems Including ATM
Discrete-Time Models for Communication Systems Including ATM
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
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This paper presents a multi-server queueing model with abandonments in discrete time. In every time slot a generally distributed number (batch) of customers arrives. The different numbers of arrivals in consecutive slots are mutually independent. Each customer requires a geometrically distributed service time. Customers arriving in a slot can start their service only at the beginning of the next slot. When upon arrival customers find all servers busy, they join a queue and wait for their service. When upon arrival customers find server(s) idle, then as many of the incoming customers (randomly chosen) start their service at the beginning of the next slot as there are idle servers, whereas the excess incoming customers, if any, join the queue. The customers in the queue are served in the order of arrival. Every time slot each customer waiting in the queue decides to abandon the system forever with a fixed (abandon) probability, i.e. independently from the other customers waiting in the queue, his position in the queue or the elapsed waiting time. Arrivals have precedence over departures. The steady-state behaviour of this system is studied.