In this paper, we present a unifying analysis for redundancy systems with cancel-on-start (c.o.s.) and cancel-on-complete (c.o.c.) with exponentially distributed service requirements. With c.o.s. (c.o.c.) all redundant copies are removed as soon as one of the copies starts (completes) service. As a consequence, c.o.s. does not waste any computing resources, as opposed to c.o.c.. We show that the c.o.s. model is equivalent to a queueing system with multi-type jobs and servers, which was analyzed in [1], and show that c.o.c. (under the assumption of i.i.d. copies) can be analyzed by a generalization of [1] where state-dependent departure rates are permitted. This allows us to show that the stationary distribution for both the c.o.c. and c.o.s. models have a product form. We give a detailed first-time analysis for c.o.s and derive a closed form expression for important metrics like mean number of jobs in the system, and probability of waiting. We also note that the c.o.s. model is equivalent to Join-Shortest-Work queue with redundancy (JSW(d)). In the latter, an incoming job is dispatched to the server with smallest workload among d randomly chosen ones. Thus, all our results apply mutatis-mutandis to JSW(d). Comparing the performance of c.o.s. with that of c.o.c. with i.i.d copies gives the unexpected conclusion (since c.o.s. does not waste any resources) that c.o.s. is worse in terms of mean number of jobs. As part of ancillary results, we illustrate that this is primarily due to the assumption of i.i.d copies in case of c.o.c. (together with exponentially distributed requirements) and that such assumptions might lead to conclusions that are qualitatively different from that observed in practice.

No abstract

Service systems using a highest-bidder-first (HBF) policy have been studied in queueing literature for various applications and in economics literature to model corruption. Such systems have applications in modern problems like scheduling jobs in cloud computing scenarios or placement of ads on web pages. However, using a HBF service is like using a spot market and may not be preferred by many users. For such users, it may be good to provide a simple scheduler, e.g., a FIFO service. Further, in some situations it may even be necessary that a free service queue operates alongside a HBF queue. Motivated by such a scenario, we propose and analyze a service system with a FIFO server and a HBF server in parallel. Arriving customers are from a heterogeneous population with different valuations of their delay costs. They strategically choose between FIFO and HBF service; if HBF is chosen, they also choose the bid value to optimize an individual cost. We characterize the Wardrop equilibrium in such a system and analyze the revenue to the server. We see that when the total capacity is fixed and is shared between the FIFO and HBF servers, revenue is maximised when the FIFO capacity is non zero. However, if the FIFO server is added to an HBF server, then the revenue decreases with increasing FIFO capacity. We also discuss the case when customers are allowed to balk.

In this paper, we present a unifying analysis for redundancy systems with cancel-onstart (c.o.s.) and cancel-on-complete (c.o.c.) with exponentially distributed service requirements. With c.o.s. (c.o.c.) all redundant copies are removed as soon as one of the copies starts (completes) service. As a consequence, c.o.s. does not waste any computing resources, as opposed to c.o.c. We show that the c.o.s. model is equivalent to a queueing system with multi-type jobs and servers, which was analyzed in Visschers et al., (2012), and show that c.o.c. (under the assumption of i.i.d. copies) can be analyzed by a generalization of Visschers et al., (2012) where state-dependent departure rates are permitted. This allows us to show that the stationary distribution for both the c.o.c. and c.o.s. models has a product form. We give a detailed first-time analysis for c.o.s and derive a closed form expression for important metrics like mean number of jobs in the system, and probability of waiting. We also note that the c.o.s. model is equivalent to Join-Shortest-Work queue with power of d (JSW(d)). In the latter, an incoming job is dispatched to the server with smallest workload among d randomly chosen ones. Thus, all our results apply mutatis-mutandis to JSW(d). Comparing the performance of c.o.s. with that of c.o.c. with i.i.d. copies gives the unexpected conclusion (since c.o.s. does not waste any resources) that c.o.s. is worse in terms of mean number of jobs. As part of ancillary results, we illustrate that this is primarily due to the assumption of i.i.d. copies in case of c.o.c. (together with exponentially distributed requirements) and that such assumptions might lead to conclusions that are qualitatively different from that observed in practice.