On the Optimal Assignment of Streams in Server

We consider a server farm with different classes of arriving requests. For each class, the request arrival rate, the mean service time and the variance of the service time are assumed to be known. The arrivals are Poisson and the service times are distributed arbitrarily. Servers are modeled a s single server queuing systems. The problem is to determine the assignment of requests’ classes to servers in order to minimize the overall expected waiting time, overall probability of the wait exceeding a given value, and related measures.

We optimize under two separate conditions. The first is the light traffic condition, and the second is the balanced load condition. In each case we obtain optimal solution for the two-server case and then based on the insights obtained we design algorithms for the multi-server case. We attempt both {\em fractional} and {\em integral} versions of the problem and show that if the number of streams is large as compared to the number of servers, then fractional and integral optimal solution values are close to each other.

The work has applications in the setting of web-server farms and E-businesses. For example, it can be used in assigning E-businesses to servers on web-server farms, or assigning customers belonging to different QoS class to different servers. Experimental results using data from actual traces show significant improvement over naive and greedy methods.

By: Rahul Garg, Perwez Shahabuddin, Akshat Verma

Published in: RI03004 in 2003


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