Derives PGF for stationary queue length, LST for system delay, and joint transform for busy cycle in gated M/GI/1 with single vacations, applied to batch-service M/G/1 queues with size-dependent service times.
A distributional form of Little’s law
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The Gated-Service M/GI/1 Queue with Single Vacations and Its Application to Batch-Service Queues
Derives PGF for stationary queue length, LST for system delay, and joint transform for busy cycle in gated M/GI/1 with single vacations, applied to batch-service M/G/1 queues with size-dependent service times.