Competitive strategies for an online generalized assignment problem with a service consecution constraint

This work studies a variant of the online generalized assignmen t problem , where there are m P 2 heterogeneous servers to process n requests which arrive one by one over time. Each request mu st either be assigned to one of the servers or be rejected upon its arrival, before knowing any information of future requests. There is a corresponding weight (or revenue) for assigning each request to a server, and the objective is to maximize the total weights obtained from all the requests. We study the abov e problem with a service consecuti on constraint , such that at any time each server is only allowe d to process up to d consecutiv e requests. We investigate both deterministic and randomized online strategies for this problem. When the ratio q between the largest and smallest possible weights obtained from assigning a request to a server is known in advance, we present an opt imal deterministic online strategy with competitive ratio q1d . For ran domized strategies, we first prove a lower bound on the competitiv e ratio, then we present a randomized strategy with competitive ratio less than 2, which does not need to know the value of q or d. Computational tests show that our proposed strategies have very good practical performance. 2013 Elsevier B.V. All rights reserved.