Stationary Waiting Time in Parallel Queues with Synchronization

Abstract

Motivated by database locking problems in today’s massive computing systems, we analyze a queueing network with many servers in parallel (files) to which jobs (writing access requests) arrive according to a Poisson process. Each job requests simultaneous access to a random number of files in the database and will lock them for a random period of time. Alternatively, one can think of a queueing system where jobs are split into several fragments that are then randomly routed to specific servers in the network to be served in a synchronized fashion. We assume that the system operates on a first-come, first-served basis. The synchronization and service discipline create blocking and idleness among the servers, which leads to a strict stability condition compared with other distributed queueing models. We analyze the stationary waiting time distribution of jobs under a many-server limit and provide exact tail asymptotics. These asymptotics generalize the celebrated Cramér–Lundberg approximation for the single-server queue.