Dispatching to parallel servers

To curb the spread of contagious diseases and the recent polio outbreak in Nigeria, health departments must set up and operate clinics to dispense medications or vaccines. Residents arrive according to an external (not necessarily Poisson) Arrival process to the clinic. When a resident arrives, he goes to the first workstation, based on his or her information, the resident moves from one workstation to another in the clinic. The queuing network is decomposed by estimating the performance of each workstation using a combination of exact and approximate models. A key contribution of this research is to introduce approximations for workstations with batch arrivals and multiple parallel servers, for workstations with batch service processes and multiple parallel servers, and for self service workstations. We validated the models for likely scenarios using data collected from one of the states vaccination clinics in the country during the vaccination exercises.

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Queueing Problems with Two Parallel Servers

Studies in Choice and Welfare - Fair Queueing ◽

10.1007/978-3-319-33771-5_10 ◽

2016 ◽

pp. 141-157

Author(s):

Youngsub Chun

Keyword(s):

Parallel Servers

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Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

Advances in Applied Probability ◽

10.1017/s0001867800009642 ◽

1999 ◽

Vol 31 (04) ◽

pp. 1095-1117 ◽

Cited By ~ 6

Author(s):

Hyun-Soo Ahn ◽

Izak Duenyas ◽

Rachel Q. Zhang

Keyword(s):

Numerical Study ◽

Stochastic Scheduling ◽

Static Case ◽

Tandem Queue ◽

Two Stage ◽

Holding Costs ◽

Parallel Servers ◽

Cross Training ◽

Dynamic Case ◽

Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

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