# American Institute of Mathematical Sciences

July  2010, 6(3): 541-568. doi: 10.3934/jimo.2010.6.541

## Analysis of multiclass feedback queues and its application to a packet scheduling problem

 1 Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba-city, Ibaraki 305-0006, Japan

Received  September 2009 Revised  April 2010 Published  June 2010

In this paper, we investigate mean sojourn times in multiclass queues with feedback and their application to packet scheduling in communication networks.
We first analyze the feedback queues with $J$ groups of customers and a single server. The server selects a group (station) in a priority order and admits its customers into the service facility according to one of the following rules: 1-limited, gated, or exhaustive. Since there are multiple classes of customers in each group, they are served in either the (local) priority order or the first-come-first-served order. We derive the mean sojourn times for all service stages of customers circulating the system.
Then we consider their application to a packet scheduling problem in communication networks where a mission-critical traffic is given some preferential treatment over other normal traffic. Packets belonging to normal traffic are allocated the resource capacity in proportion to their assigned weights in a round-robin manner, which we call the "discriminatory round robin (DRR)." We construct some composite scheduling algorithms and compare their performance.
Citation: Tetsuji Hirayama. Analysis of multiclass feedback queues and its application to a packet scheduling problem. Journal of Industrial & Management Optimization, 2010, 6 (3) : 541-568. doi: 10.3934/jimo.2010.6.541
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