Large Deviations without Principle: Join the Shortest Queue

Arbeitspapier

We develop a methodology for studying large deviations type questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are routed to the (weighted) shortest queue. It is not known whether the large deviations principle holds for this system. Using the tools developed here we derive large deviations type estimates for the most likely behavior, the most likely path to overflow and the probability of overflow. The analysis applies to any finite number of queues. We show via a counterexample that this sytem may exhibit unexpected behavior.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 05-003/4

Classification and Topics

• Classification: Wirtschaft ; Existence and Stability Conditions of Equilibrium ; Miscellaneous Mathematical Tools
• Subject: Sample path large deviations ; rate function ; optimal paths ; Warteschlangentheorie ; Mathematische Optimierung

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Ridder, Ad ; Shwartz, Adam
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2004

Further information

• Handle: http://hdl.handle.net/10419/86466
• Last update: 10.03.2025, 11:42 AM CET