Dynamic Assignment of Dedicated and Flexible Servers in Tandem Lines

Abstract

Consider a system of queuing stations in tandem having both flexible servers (who are capable of working at multiple stations) and dedicated servers (who can only work at the station to which they are dedicated). We study the dynamic assignment of servers to stations in such systems with the goal of maximizing the long-run average throughput. We also investigate how the number of flexible servers influences the throughput and compare the improvement that is obtained by cross-training another server (i.e., increasing flexibility) with the improvement obtained by adding a resource (i.e., a new server or a buffer space). Finally, we show that having only one flexible server is sufficient for achieving near-optimal throughput in certain systems with moderate to large buffer sizes (the optimal throughput is attained by having all servers flexible). Our focus is on systems with generalist servers who are equally skilled at all tasks, but we also consider systems with arbitrary service rates.Ayhan, and Down [6][7][8], and Tassiulas and Bhattacharya [29] considered the dynamic assignment of servers to maximize the long-run average throughput in queuing networks with flexible servers. However, these articles do not focus on the case where some servers are dedicated to specific stations.Ostalaza, McClain, and Thomas [23], McClain, Thomas, and Sox [22], Zavadlav, McClain, and Thomas [34], and, more recently, Ahn and Righter [4] have considered using server flexibility to achieve dynamic line balancing. More specifically, Ostalaza et al. [23] and McClain et al. [22] studied dynamic line balancing in tandem queues with shared tasks that can be performed at either of two successive stations. This work was continued by Zavadlav et al. [34], who studied several server assignment policies for systems with fewer servers than stations, in which all servers trained to work at a particular station have the same capabilities at that station. Ahn and Righter [4] studied how workers who are trained to do a set of consecutive tasks should be assigned dynamically to tandem stations. Bartholdi and Eisenstein [9] defined the "bucket brigades" server assignment policy for systems in which each server works at the same rate at all tasks and showed that under this policy, a stable partition of work will emerge yielding optimal throughput. Bartholdi, Eisenstein, and Foley [10] showed that the behavior of the bucket brigades policy, applied to systems with discrete tasks and exponentially distributed task times, resembles that of the same policy applied in the deterministic setting with infinitely divisible jobs.Gurumurthi and Benjaafar [14], Hopp, Tekin, and van Oyen [17], and Sheikhzadeh, Benjaafar, and Gupta [27] considered the use of specific flexibility structures on a set of existing servers to enhance the system's performance (see also Jordan and Graves [19] for related work). More specifically, Gurumurthi and Benjaafar [14] considered the modeling and analysis of flexible queuing systems. They illustrated that for systems with identi...

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

“…However, the threshold value where the moving server switches from station 1 to station 2 now also depends on the status of the other servers. For longer tandem lines with generalist servers, Andradóttir, Ayhan, and Down [4] showed that any non-idling server assignment policy is optimal. We generalize this result and prove that any non-idling policy (in which servers idle only when they are down) is still optimal when the servers are subject to failures.…”

Optimal assignment of servers to tasks when collaboration is inefficient

“…In the interest of space, we do not provide a complete literature review here, but refer the interested reader to Hopp and Van Oyen [13] for a comprehensive review of the literature in this area, and to Akşin, Armony, and Mehrotra [4], Akşin, Karaesmen, andÖrmeci [5], and Gans, Koole, and Mandelbaum [12] for thorough reviews of the literature on flexible servers in call centers. This paper is most closely related to other works that employ Markov decision process techniques and sample path analysis in determining effective server allocation schemes, see for example Ahn, Duenyas, and Zhang [1], Ahn and Lewis [2], Ahn and Righter [3], Andradóttir and Ayhan [6], Andradóttir, Ayhan, and Down [7,8], Kaufman, Ahn, and Lewis [15],Örmeci [17], Sennott, Van Oyen, and Iravani [19], Van Oyen, Gel, and Hopp [20], and Wu, Lewis, and Veatch [21]. However, these papers only consider cases where the combined rate of a set of collaborating servers is additive (i.e., α = 1).…”

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

“…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.…”