Hysteretic capacity switching for M/G/1 queues

Abstract

{We study (in M/G/1 system with finite workload capacity that can be switched between two capacity levels v* < v**}. Whenever the workload process {V(t) >= 0} is about to exceed the current capacity, the excess service time is truncated. We consider hysteretic control policies with two trigger points 0 < v(L) < v(U) < (vempty set) where switching from v* to v**} takes place when V(t) upcrosses vu; when V(t) drops down to v(L). the capacity is switched back from v**} to v*. We derive formulae for the expected total discounted cost of switching and maintaining extra capacity as well as the total expected discounted loss of discarded service. These functionals determine whether switching between capacities can achieve a net gain. The total expected discounted cost of holding service request's in the system is also derived. hin M/M/1 queues we obtain simplified results in terms of elementary functions and provide numerical examples, which indicate that hysteretic capacity control can lead to substantial savings.}