Delay, memory, and messaging tradeoffs in distributed service systems

Distributed service systems such as data-centers and multi-core processors have enabled the exponential growth of the network infrastructure that supports the Internet. From the point of view of an administrator of such systems, the objective is to provide the best possible service to the customers (fast response times), using the least possible amount of control overhead. This type of systems can be analyzed using the following stylized model: a single stream of jobs arrive as a Poisson process of rate L.N, with 0L1 fixed, and are immediately dispatched to one of several queues associated with N identical servers with unit processing rate. We assume that the dispatching decisions are made by a central dispatcher endowed with a finite memory, and with the ability to exchange messages with the servers. In this setting, we study the fundamental resource requirements (in terms of memory bits and message exchange rate), in order to drive the expected steady-state queueing delay of a typical job to zero, as N increases. We propose a certain policy and establish that it drives the delay to zero when either (i) the message rate grows superlinearly with N, or (ii) the memory grows superlogarithmically with N. Moreover, we show that any policy that has a certain symmetry property, and for which neither condition (i) or (ii) holds, results in an expected queueing delay which is bounded away from zero.
Martin Zubeldia is a 5th year PhD student in Electrical Engineering at MIT, co-advised by Profs. John N. Tsitsiklis and David Gamarnik. His research interests lie in the field of applied probability, seeking to understand fundamental properties and design principles of large-scale stochastic systems, with applications in computer networks, communications, distributed learning, and other service systems.