Equilibrium and Optimal Strategies for Placing Duplicate Orders in Queues
Posted: 26 Mar 2012
Date Written: February 8, 2012
We consider strategic behavior and the socially optimal requirements for customers to place duplicate orders with the intention of speeding up their service. We first study a situation in which customers place duplicate orders in a one-server, random order service system. We demonstrate that follow-the-crowd (FTC) behavior exists and that two pure equilibria and one mixed equilibrium could exist in the order size. We then study another situation in which customers place duplicate orders in two parallel queues. For symmetric servers with the same service rates and ordering costs, we show that avoid-the-crowd (ATC) behavior exists and we characterize a unique equilibrium. Comparing the equilibrium to socially optimal behavior reveals that the equilibrium arrival rate of duplicate-order customers is larger than socially desired when the ordering cost is low and smaller when the ordering cost is high. For asymmetric servers, a customer has three choices: join the first queue, join the second queue or join both queues simultaneously. Our numerical results suggest that pairwise ATC holds; that is, if one of these three actions is fixed, customers exhibit ATC behavior in the remaining two actions. Our numerical study shows that the main conclusions in the symmetric-server case still hold in the asymmetric-server case. Methodologically, we provide an innovative approach to solving problems in queues with simultaneous arrivals and departures in a closed-form.
Keywords: Duplicate order, queues with instantaneous movements, equilibrium analysis, strategic customers
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