Optimizing static calendar queues

Authors:
K. B. Erickson;R. E. Ladner;A. LaMarca
Affiliations:
Washington Univ., Seattle, WA, USA;Washington Univ., Seattle, WA, USA;Washington Univ., Seattle, WA, USA
Venue:
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Year:
1994

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Abstract

The calendar queue is an important implementation of a priority queue which is particularly useful in discrete event simulators. In this paper we present an analysis of the static calendar queue which maintains N active events. A step of the discrete event simulator removes and processes the event with the smallest associated time and inserts a new event whose associated time is the time of the removed event plus a random increment with mean /spl mu/. We demonstrate that for the infinite bucket calendar queue the optimal bucket width is approximately /spl delta//sub opt/=/spl radic/(2b/c)/spl mu//N where b is the time to process an empty bucket and c the incremental time to process a list element. With bucket width chosen to be /spl delta//sub opt/, the expected time to process an event is approximately minimized at the constant c+/spl radic/(2bc)+d, where d is the fixed time to process an event. We show that choosing the number of buckets to be O(N) yields a calendar queue with performance equal to or almost equal to the performance of the infinite bucket calendar queue.