A nearly-optimal index rule for scheduling of users with abandonment

—We analyze a comprehensive model for multi-class job scheduling accounting for user abandonment, with the objective of minimizing the total discounted or time-average sum of linear holding costs and abandonment penalties. We assume geometric service times and Bernoulli abandonment probabilities. We solve analytically the case in which there are 1 or 2 users in the system to obtain an optimal index rule. For the case with more users we use recent advances from the restless bandits literature to obtain a new simple index rule, denoted by AJN, which we propose to use also in the system with arrivals. In the problem without abandonment, the proposed rule recovers the cµ-rule which is well-known to be optimal both without and with arrivals. Under certain conditions, our rule is equivalent to the cµ/θ-rule, which was recently proposed and shown to be asymptotically optimal in a multi-server system with overload conditions. We present results of an extensive computational study that sug...

• Type: Journal
• Year: 2011
• Where: INFOCOM
• Authors: Urtzi Ayesta, Peter Jacko, Vladimir Novak
• Keywords: Communications, INFOCOM 2011, Optimal Index, Overload Conditions, Restless Bandits