Optimal Bandwidth Allocation in a Delay Channel

In this paper, we consider the problem of allocating bandwidth to two queues with arbitrary arrival processes, so as to minimize the total expected packet holding cost over a finite or infinite horizon. Bandwidth is in the form of time slots in a time-division multiple-access schedule. Allocation decisions are made based on one-step delayed queue backlog information. In addition, the allocation is done in batches, in that a queue can be assigned any number of slots not exceeding the total number in a batch. We show for a two queue system that if the holding cost as a function of the packet backlog in the system is nondecreasing, supermodular, and superconvex, then: 1) the value function at each slot will also satisfy these properties; 2) the optimal policy for assigning a single slot is of the threshold type; and 3) optimally allocating slots at a time can be achieved by repeatedly using a policy that assigns each slot optimally given the previous allocations. Thus, the problem of find...

• Type: Journal
• Year: 2006
• Where: JSAC
• Authors: Navid Ehsan, Mingyan Liu
• Keywords: Holding Cost, JSAC 2006, One-step Delayed Queue, Packet Holding Cost