OPTIMAL CONTROL POLICIES FOR AN M/M/1 QUEUE WITH A REMOVABLE SERVER AND DYNAMIC SERVICE RATES. Issue 2 (April 2021)

• Record Type: Journal Article
• Authors: Badian-Pessot, Pamela; Lewis, Mark E.; Down, Douglas G.
• Is Part Of: Probability in the engineering and informational sciences. Volume 35:Issue 2(2021)
• Page Start: 189
• Page End: 209
• Publication Date: 2021-04
• Subjects: applied probability, -- queueing theory, -- stochastic dynamic programming; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964819000299
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract: We consider an M / M /1 queue with a removable server that dynamically chooses its service rate from a set of finitely many rates. If the server is off, the system must warm up for a random, exponentially distributed amount of time, before it can begin processing jobs. We show under the average cost criterion, that work conserving policies are optimal. We then demonstrate the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number in system. Finally, we present some numerical experiments to provide insights into the practicality of having both a removable server and service rate control.