We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In single-server k=1 case, optimal policy is Gittins policy, but it not known whether or any other in multiserver case. Exactly analyzing under intractable, and a particularly complicated that hard analyze even this work we introduce monotonic (M-Gittins), new variation show minimizes heavy-traffic ...

We consider an M/G/1 queue with a removable server. When a customer arrives, the workload becomes known. The cost structure consists of switching costs, running costs, and holding costs per unit time which is a nonnegative nondecreasing right-continuous function of a current workload in the system. We prove an old conjecture that D-policies are optimal for the average cost per unit time criteri...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

This paper identifies various parametrized dynamic priority queue disciplines from literature which are complete in two class M/G/1 queue. Equivalence between these queue disciplines is established by obtaining non linear transformation in closed form. Motivation behind these completeness and equivalence results is discussed from optimal control perspective. Some comments on global FCFS policy ...