A proof of the conjecture in "Pricing surplus server capacity for mean waiting time sensitive customers"

Abstract

This paper settles the conjecture of Sinha, Rangaraj and Hemachandra (2010) [12], on a joint pricing and scheduling problem. The overall objective of this problem is to optimally price the server's surplus capacity by introducing price and mean waiting time sensitive new (secondary) class of customers that also satisfy the predefined service level requirement of the existing (primary) class of customers. The optimal pricing and scheduling parameters depend on the solution of two optimization problem and the conjecture is in the context of comparison of these two objective functions for a certain finite range of service level. Thus, the finite step algorithm (assuming conjecture is true) in Sinha, Rangaraj and Hemachandra (2010) [12] to obtain optimal pricing and operating parameters is valid. The above model can be used to capture strategic interaction between service-provider (as a queue) and user-set (customers).