On the price of anarchy in a single-server queue with heterogeneous service valuations induced by travel costs

2018 ◽  
Vol 265 (2) ◽  
pp. 580-588 ◽  
Author(s):  
Refael Hassin ◽  
Irit Nowik ◽  
Yair Y. Shaki
Keyword(s):  
Price Of Anarchy ◽  
Single Server ◽  
Single Server Queue ◽  
Travel Costs ◽  
Server Queue ◽  
Heterogeneous Service

scholarly journals The Benefit of Information in a Single-server Queue with Heterogeneous Service Valuations [Abstract]

10.28945/4356 ◽  
2019 ◽  
Keyword(s):  
Queue Length ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Future Research ◽  
Single Server ◽  
Single Server Queue ◽  
Travel Costs ◽  
Control Of Queues ◽  
Server Queue ◽  
Heterogeneous Service

Aim/Purpose: How does heterogeneous valuation of service affect optimal control of queues? Background We analyze this heterogeneity by adding a component of travel costs, which differ with distance from the service point. Methodology: Mathematical analysis of queuing theory. Analyzing the anarchy function. Contribution: Enabling consumers to make optimal choices based on knowledge about their status, and enabling better control of the organizer. Findings: In the arrival rate is bounded, there is no need of interference. If it is unbounded then in many cases the organizer should impose the socially optimal queue length. Recommendations for Practitioners: In the arrival rate is bounded, there is no need of interference. If it is unbounded then in many cases the organizer should impose the socially optimal queue length. Recommendations for Researchers: Explore the following points: What happens when there are more than one server, located at different point. How should consumers behave, and what is the best way to locate service points. Impact on Society: Handling queues taking into account social welfare. Future Research: What happens when there are more than one server, located at different point. How should consumers behave, and what is the best way to locate service points.

scholarly journals The Price of Anarchy in the Markovian Single Server Queue

2014 ◽  
Vol 59 (2) ◽  
pp. 455-459 ◽  
Author(s):  
Gail Gilboa-Freedman ◽  
Refael Hassin ◽  
Yoav Kerner
Keyword(s):  
Price Of Anarchy ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

scholarly journals New Approach for Finding Basic Performance Measures of Single Server Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Siew Khew Koh ◽  
Ah Hin Pooi ◽  
Yi Fei Tan
Keyword(s):  
Stationary State ◽  
Queue Length ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
System Capacity ◽  
Interarrival Time ◽  
Single Server ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functionf(t)and the cumulative distribution functionF(t)of the interarrival time are such that the ratef(t)/1-F(t)tends to a constant ast→∞, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.

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