Optimal assignment of servers to tasks when collaboration is inefficient

Abstract

Consider a Markovian system of two stations in tandem with finite intermediate buffer and two servers. The servers are heterogeneous, flexible, and more efficient when they work on their own than when they collaborate. We determine how the servers should be assigned dynamically to the stations with the goal of maximizing the system throughput. We show that the optimal policy depends on whether or not one server is dominant (i.e., faster at both stations) and on the magnitude of the efficiency loss of collaborating servers. In particular, if one server is dominant then he must divide his time between the two stations and we identify the threshold policy the dominant server should use; otherwise each server should focus on the station where he is the faster server. In all cases, servers only collaborate to avoid idleness when the first station is blocked or the second station is starved, and we determine when collaboration is preferable to idleness as a function of the efficiency loss of collaborating servers.

Optimal Dynamic Allocation of Collaborative Servers in Two Station Tandem Systems

“…which follows fromd(1, 0) >d(1, 1), g(0, x2) being decreasing, and Lemma 2. For x2 ≥ 2,d(1, x2) −d(1, x2 + 1) > 0 is proved by a straightforward induction on x2 based on (17). We now turn to the proof of part (ii) .…”

“…In addition to partially collaborating servers (subadditive rates) they considered the case when collaboration increases the servers' efficiency, that is, their combined service rate is larger than the sum of their individual rates (superadditive rates). Models with non-additive rates for tandem systems with throughput maximization as the objective were studied by Andradottir, Ayhan, and Down [17] (subadditive rates), Andradottir, Ayhan, and Down [18] and Wang, Andradottir, and Ayhan [19] (superadditive rates). For 0018-9286 (c) 2018 IEEE.…”

Bloody fast blood collection

“…The paper also includes a heuristic policy that preforms near-optimal for these non-exponential systems. This work has inspired many papers that focus on throughput maximization; some examples of this work can be found in [10,11,13,17,18,48,106,120,177].…”

Optimization of flexible production and supply systems

“…Parvin et al [63] presented a zone chaining pattern with limited cross-training that can achieve high throughput. Finally, for models limited to 2 or 3 stages, throughput maximizing policies were determined by Andradottir et al [8], [9], [10], [12], Andradottir and Ayhan [7], Gel et al [29], Arumugam et al [14], Hasenbein and Kim [33], Kirkizlar et al [44], and Wang et al [83].…”

“…In addition to partially collaborating servers (subadditive rates) they considered the case when collaboration increases the servers' efficiency, that is, their combined service rate is larger than the sum of their individual service rates (superadditive rates). Models with non-additive rates for tandem systems with throughput maximization as the objective were studied by Andradottir et al [12] (subadditive rates), Andradottir et al [10] and Wang et al [83] (superadditive rates). In the context of tandem systems with dedicated servers in each station it will become evident from the analysis that the problem with superadditive service rates is equivalent to a problem with fully collaborative servers, so we do not consider this case.…”