The M^θ /G/1/m queues with the time of service, depending on the length of the queue (in Ukrainian)

Abstract

We study the M^θ /G/1/m queue with the time of service, depending on the length of the queue at the service initiation. By using Korolyuk's potential method, we derive the average duration of the busy time and the stationary distribution of the number of customers in such a system. Similar results for the M^θ /G/1/m queue with one threshold of switching of service modes are obtained.

Keywords

• M^theta/G/1/m queue
• queue length dependent service time
• stationary distribution of the number of customers