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Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek toreap benefits of parallelization, albeit subject to a synchronizationconstraint at the output. Fork-Join (FJ) queuing models are used to analyzesuch systems. Arriving jobs are split into tasks each of which is mapped toexactly one server. A job leaves the system when all of its tasks are executed.  As a metric of performance, we consider waiting times for bothwork-conserving and non-work conserving server systems under a mathematicalset-up general enough to take into account possible phase-type behavior of theservers, and as suggested by recent evidences, bursty arrivals.  To this end, we present a Markov-additive process framework for an FJ systemand provide computable bounds on tail probabilities of steady-state waitingtimes, for both types of servers separately. We apply our results to threescenarios, namely, non-renewal (Markov-modulated) arrivals, servers showingphase-type behavior, and Markov-modulated arrivals and services. We compare ourbounds against estimates obtained through simulations and also provide atheoretical conceptualization of provisions in FJ systems. Finally, wecalibrate our model with real data traces, and illustrate how our bounds can beused to devise provisions.

A Generalized Performance Evaluation Framework for Parallel Systems with Output Synchronization