Heavy-traffic Limits For Many-server Queues With Service Interruptions

Queues are widely used in our production, our daily life, and our technology. With the progress of science and technology and people living standard rise, the demand for service system is also increased. But there will be service interrptioOn when the server is always running, infrequent service interruptions can have a dramatic impact on the queue system,so the study of models with service interruptions is necessary.In order to study the impact of service interruptions on the performance of queueing system, we establish heavy-traffic stochastic-process limits for waiting time in the G/M/n+M queues with service interruptions. In the G/M/n+M queues with service interruptions, when the system is asymptotically critically loaded or not asymptotically critically loaded in fluid scale, heavy-traffic limits for virtual waiting times in the queueing systems can deduce using the Puhalskii's invariance principle for the first-passage times.The conclusion shows that the customer's virtual waiting time is closely related to the queue-length process.There are two types of scaling for the service interruption durations: unsealed and asymptotically negligible. With the unsealed and asymptotically negligible service interruptions, we obtain the heavy-traffic limits for queue-length processes, and we apply these results here to establish heavy-traffic stochastic-process limits for waiting time in the G/M/n + M queues with service interruptions.On the basis of G/M/n + M queues with service interruption, we apply its results to get the heavy-traffic stochastic-process limits for virtual waiting time and steady-state virtual waiting time in the M/M/n + M queues with asymptotically negligible service interruptions.Finally, we generalize the G/M/n + M queues with service interruptions, we establish heavy-traffic stochastic-process limits for the queue-length in the G/M/n + M queues with service interruptions.