In cloud computing systems, assigning a task to multiple servers and waiting for the earliest copy to finish is an effective method to combat the variability in response time of individual servers, and thus reduce average latency. But adding redundancy may result in higher cost of computing resources, as well as an increase in queueing delay due to higher traffic load. This work helps understand when and how redundancy gives a cost-efficient reduction in latency. For a general task service time distribution, we compare different redundancy strategies, for e.g. the number of redundant tasks, and time when they are issued and canceled. We get the insight that the log-concavity of the task service distribution is a key factor in determining whether adding redundancy helps. If the service distribution is log-convex, then adding maximum redundancy reduces both latency and cost. And if it is log-concave, then less redundancy, and early cancellation of redundant tasks is more effective. Using these insights, we design a general redundancy strategy that achieves a good latency-cost trade-off for an arbitrary service distribution. This work also generalizes and extends some results in the analysis of fork-join queues.
Advance reservation (AR) services form a pillar of several branches of the economy, including transportation, lodging, dining, and more recently, cloud computing. In this work, we use game theory to analyze a slotted AR system in which customers differ in their lead times. For each given time slot, the number of customers requesting service is a random variable following a general probability distribution. Based on statistical information, the customers decide whether or not making an advance reservation of server resources in future slots for a fee. We prove that only two types of equilibria are possible: either none of the customers makes AR or only customers with lead time greater than some threshold make AR. Our analysis further shows that the fee that maximizes the provider's profit may lead to other equilibria, one of which yielding zero profit. In order to prevent ending up with no profit, the provider can elect to advertise a lower fee yielding a guaranteed, but smaller profit. We refer to the ratio of the maximum possible profit to the maximum guaranteed profit as the price of conservatism.