Equilibrium and Optimization in a Double-Ended Queueing System with Dynamic Control

Abstract

In this paper, we consider a double-ended queueing system which is a passenger-taxi service system. In our model, we also consider the dynamic taxi control policy which means that the manager adjusts the arrival rate of taxis according to the taxi stand congestion. Under three different information levels, we study the equilibrium strategies as well as socially optimal strategies for arriving passengers by a reward-cost structure. Furthermore, we present several numerical experiments to analyze the relationship between the equilibrium and socially optimal strategies and demonstrate the effect of different information levels as well as several parameters on social benefit.

Equilibrium Behaviour of Double-Sided Queueing System with Dependent Matching Time

“…In this section, key results from Wang and Liu [18] are given. More detailed proofs are provided and results are simplified.…”

“…, and ρ 2 = λ 1 q λ 2 . From Wang and Liu [18], we have the stationary probabilities of the double-ended system with dynamic control for the partially observable case given as:…”

“…The double-ended queueing model was first considered by Kendall This way, the system can be modeled as a modified birth and death process where the state may be negative. In some cases, such as in Wang and Liu [18], the system is similar to a truncated birth and death process which is shifted so that the state space begins at −N , the taxi waiting capacity, rather than 0.…”

“…The study developed in this thesis is an extension of the taxi-passenger doubleended queue model presented by Wang and Liu [18] which used dynamic controls for taxi arrival times depending on the state of the passenger queue. This model will be extended in this thesis by including non-zero matching time to the analysis.…”

“…The model considered in this paper is a double-ended queue with state space Wang and Liu [18] analyzed the utility function for a passenger and the social welfare function for both passengers and taxis given passenger joining probability CHAPTER 2. DOUBLE-ENDED TAXI-PASSENGER QUEUEING SYSTEM14…”