Queueing problems with two parallel servers

Arbeitspapier

A group of agents are waiting for their job to be processed in a facility. We assume that each agent needs the same amount of processing time and incurs waiting costs. The facility has two parallel servers, being able to serve two agents at a time. We are interested in finding the order to serve agents and the (positive or negative) monetary compensations they should receive. We introduce two rules for the problem, the minimal transfer rule and the maximal transfer rule. We show that these two rules correspond to the Shapley (1953) value of the queueing games with two servers, as discussed similarly by Maniquet (2003) and Chun (2006a) for queueing problems with one serve, when the worth of each coalition is appropriately defined. If the worth of a coalition is defined by assuming the coalitional members are served before the non-coalitional members, then the minimal transfer rule is obtained. On the other hand, if it is defined by assuming the coalitional members are served after the non-coalitional members, then the maximal transfer rule is obtained.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: ISER Discussion Paper ; No. 683

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games ; Equity, Justice, Inequality, and Other Normative Criteria and Measurement ; Bureaucracy; Administrative Processes in Public Organizations; Corruption
• Subject: queueing problems with two servers ; Shapley value ; minimal transfer rule ; maximal transfer rule ; Warteschlangentheorie ; Shapley-Wert ; Kooperatives Spiel

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Chun, Youngsub ; Heo, Eun Jeong
• Event: Veröffentlichung
• (who): Osaka University, Institute of Social and Economic Research (ISER)
• (where): Osaka
• (when): 2007

Further information

• Handle: http://hdl.handle.net/10419/92586
• Last update: 10.03.2025, 11:45 AM CET