A lower bound for mean characteristics in E_k/G/1 and GI/E_k/1 queues¹

¹This research supported in part by AFOSR Contract No. F 49620 82 C 0009 at the Center for Stochastic Processes, University of North Carolina, Chapel Hill, N.C., U.S.A.

Abstract

The mean stationary waiting time EW of a stable E _k /G/1 queueing system depends on the service distribution through its first two moments and k–1 roots of an equation involving its transform. Vainshtein's (1983) work on delimiting the region where such roots lie is improved and leads to a bound on EW that is always tighter than other known lower bounds. The methods can also be applied to Gi/E _k /1 systems but the bounds are not as useful

Keywords:

• Single Server Queueing System
• Mean Waiting Time Inequality

¹This research supported in part by AFOSR Contract No. F 49620 82 C 0009 at the Center for Stochastic Processes, University of North Carolina, Chapel Hill, N.C., U.S.A.

¹This research supported in part by AFOSR Contract No. F 49620 82 C 0009 at the Center for Stochastic Processes, University of North Carolina, Chapel Hill, N.C., U.S.A.

Notes

¹This research supported in part by AFOSR Contract No. F 49620 82 C 0009 at the Center for Stochastic Processes, University of North Carolina, Chapel Hill, N.C., U.S.A.