Batch Arrival Processor-Sharing with
Application to Multi-Level
K. Avrachenkov, U. Ayesta
, P. Brown
We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the
integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping
principle, we demonstrate the existence and uniqueness of a solution to the integral equation.
Then we provide asymptotical analysis as well as tight bounds for the expected response time
conditioned on the service time. In particular, the asymptotics for large service times depends
only on the first moment of the service time distribution and on the first two moments of the
batch size distribution. That is, similarly to the Processor-Sharing with single arrivals, in the
Processor-Sharing queue with batch arrivals the expected conditional response time is finite even
when the service time distribution has infinite second moment. Finally, we show how the present
results can be applied to the Multi-Level Processor-Sharing scheduling.
/G/1, Processor-Sharing, Batch arrivals, Work conservation, Multi-level Processor-