Optimal revenue management in two class pre-emptive delay dependent Markovian queues

In this paper, we present a comparative study on the total revenue generated with pre-emptive and non pre-emptive priority scheduler for a fairly generic problem of pricing the server's surplus capacity in a single server Markovian queue. The specific problem is to optimally price the server's surplus capacity by introducing a new class of customers (secondary class) without affecting the pre-specified service level of its current customers (primary class) when pre-emption is allowed. Pre-emptive scheduling is used in various applications. First, a finite step algorithm is proposed to obtain global optimal operating and pricing parameters for this problem. These optimal operating and pricing parameters constitute a unique Nash equilibrium in a certain two player non cooperative game. We then describe the range of service level where pre-emptive scheduling gives feasible solution and generates some revenue while non pre-emptive scheduling has infeasible solution. Further, some complementary conditions are identified to compare revenue analytically for certain range of service level where strict priority to secondary class is optimal. Our computational examples show that the complementary conditions adjust in such a way that pre-emptive scheduling always generates more revenue. Theoretical analysis is found to be intractable for the range of service level when pure dynamic policy is optimal. Hence, extensive numerical examples are presented to describe different instances. It is noted in numerical examples that pre-emptive scheduling generates at least as much revenue as non pre-emptive scheduling. A certain range of service level is identified where improvement in revenue is quite significant.