Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Abstract

Consider a tandem queueing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stations with the goal of maximizing the long-run average throughput. Our main conclusion is that the presence of server failures does not have a major impact on the optimal assignment of servers to stations for the systems we consider. More specifically, we show that when the servers are generalists, any non-idling policy is optimal, irrespective of the reliability of the servers. We also provide theoretical and numerical results for Markovian systems with two stations and two or three servers that suggest that the structure of the optimal server assignment policy does not depend on the reliability of the servers, and that ignoring server failures when assigning servers to stations yields near-optimal throughput. Finally, we present numerical results that illustrate that simple server assignment heuristics designed for larger systems with reliable servers also yield good throughput performance in Markovian systems with three stations and three failure-prone servers.

Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines

“…Hence, the threshold for server 2 (the state where server 2 starts working at station 2) is either 1 or 2 in both cases, but the value of the threshold may be different in Markovian and deterministic systems (e.g., for the system with µ 11 = µ 32 = 2, µ 12 = µ 22 = 1, µ 21 = 0.5, and µ 31 = 0.1, we have r 0.94 and r M 1.08). This is consistent with the results of Andradóttir et al [10] for Markovian systems with server failures, where the optimal policy was found to be of threshold type (as for systems without server failures), with the value of the threshold depending on the server failures. Together these results suggest that the optimality of the threshold policy of Andradóttir and Ayhan [5] is quite robust to the assumptions it is derived under, but the value of the threshold must be determined using the parameters of the problem at hand.…”

“…Andradóttir and Ayhan [5] characterized the optimal server assignment policy for Markovian systems with two stations and more than two flexible servers, and Andradóttir et al [10] considered the effects of server failures in the same settings.…”

Optimal Control of a Two-Server Queueing System With Failures

“…They provided heuristic, round-robin policies to maximize the throughput. Andradóttir, Ayhan and Down [2] considered a tandem queueing network with unreliable servers and showed that server unreliability does not change the structure of the optimal policy in some specific cases. They first considered a tandem queue with arbitrary numbers of stations and unreliable servers (which are generalists).…”

Throughput maximization for two station tandem systems: a proof of the Andradóttir–Ayhan conjecture

“…service times. The result is extended in [7] to include networks with failure-prone servers. Clearly, any tandem network with only one server satisfies the "generalist" condition.…”

“…Sennott et al [15] analyze tandem production lines with multiple servers, dedicated servers The work most closely related to this paper involve maximizing throughput in tandem queues. Apart from [2] and [3] which are described in detail above, Andradottir et al also investigated tandem lines with flexible and dedicated servers [6], failure prone servers [7], and synergistic servers [8]. Kirkizlar et al [12] analyze a tandem production line which is understaffed, i.e., there are more stations than servers.…”