Abstract We present an analytic technique for modeling load balancing policies on a cluster of servers conditioned on the fact that the arriving tasks are drawn from heavy tail distributions. We propose a new modeling methodology for the exact solution of an M/Hk/1 server and illustrate its use for modeling two distinct load balancing policies in a distributed multi-server system. Our analytic results provide exact information regarding the distribution of task sizes that compose the waiting queue on each server and suggest an easy and inexpensive way to provide load balancing based on the sizes of the incoming tasks. 1 Introduction We consider the resource allocation problem in a distributed multi-server system. We assume that tasks arrive to a front-end system, which is responsible for dispatching them to the back-end nodes. This happens according to a task scheduling policy that aims to route the request to the &quot;best &quot; back-end server, since a task can potentially be served by any server. Such a system can be considered as an abstraction of a distributed web server [7, 10, 19]. Balancing the load across the back-end servers is critical for performance . In the past two decades, there has been a significant research effort in task scheduling and load balancing (see  and references therein). The basic assumption in much of this work is that the service demands of the various tasks are governed by an exponential distribution. In contrast to the above assumption, there is very strong evidence that the size of web documents, and accordingly their service demands, are governed by heavy-tailed distributions [3, 4, 1, 2]. As a consequence, load balancing in distributed servers must be re-examined
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