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Dynamic page migration with stochastic requests

The page migration problem is one of subproblems of data management in networks. It occurs in a distributed network of processors sharing one indivisible memory page of size D. During runtime, the processors access a unit of data from the page, and the system is allowed to migrate the page between the processors. The problem is to compute (on-line) a schedule of page movements to minimize the total communication cost.The Dynamic Page Migration problem is an extension to the page migration. It attempts to model the network dynamics, occurring, for example, in mobile networks. However, the pace of changes is restricted, i.e. the distances between processors can change only by a constant per round. The movement of the nodes induce changes in the communication cost between each pair of nodes, which is proportional to the distance between them raised to some power α. This is typical for mobile wireless networks, where nodes can move with a constant speed, and the cost of communication is measured in terms of energy used for sending the data. Thus, by setting α equal to the propagation exponent of the medium, cost minimization becomes minimizing the total energy consumption in the system.However, as proven in [7], if both network mobility and request sequence are created by an adversary, then the competitive ratio is polynomially large in D and in the number of the nodes. In our search for a reasonable, close-to-reality model, in this paper we consider a scenario in which the network mobility is adversarial, but the requests are generated randomly by a stochastic process. We design an algorithm MTFR for this scenario, and prove that it is O(1)-competitive, on expectation and with high probability.