Event Lists Refs: Sections 2.2 and 2.8 in Law, Section 5.3 in - PowerPoint PPT Presentation

Event Lists Refs: Sections 2.2 and 2.8 in Law, Section 5.3 in Leemis and Park Peter J. Haas CS 590M: Simulation Spring Semester 2020 1 / 9

Event Lists Overview Linked Lists Heaps Hybrid Data Structures 2 / 9

Event Lists (aka Pending Event Sets) Fetch-next, insert, and cancel operations I Fundamental operations in discrete-event simulations (up to 40% of sim time) I So far we have used clock-reading vectors I For M events, it takes O ( M ) time to get next event I Unsuitable for large-scale simulation Alternative: event lists I For GSMP’s with unit speeds I Idea: Maintain list of (event type, event time) pairs I event time = (absolute) time when event is scheduled to occur I Challenge: support operations e ffi ciently (priority queue with removals) 3 / 9

⇐ Linked Lists Goal: Maintain events in sorted order I Singly-linked lists ÷ head tail 20.3 23.7 34.0 I fetch-next is O (1), insert and cancel are O ( M ) I Doubly-linked lists head tail . 20.3 23.7 34.0 4 / 9

Linked Lists, Continued I Indexed doubly-linked lists head tail 20.3 23.7 34.0 23.7 I Faster lookup I Need to maintain median element I Cost outweighs benefit for more than one index 5 / 9

Implicit Binary Heaps Binary tree that maintains min-heap property I Parent has smaller value than children I Can store e ffi ciently as an array I Fetch-next is O (1) plus an O (log M ) update 1.6 2.3 3.1 2.5 2.3 2.5 2.3 2.5 3.1 3.7 2.9 4.2 3.1 3.7 2.9 4.2 3.7 2.9 4.2 6 / 9

Heaps, Continued I Insert is O (log M ) 2.3 2.3 2.1 2.5 3.1 2.5 2.1 2.5 2.3 3.7 2.9 4.2 2.1 3.7 2.9 4.2 3.1 3.7 2.9 4.2 3.1 I Cancellation is O ( M ) search + O (log M ) update I Python solution for O (1) cancellation 2.1 I Use heapq to implement heap I Use a dict for O (1) find 2.5 2.3 I Mark event as ”canceled ”and I Ignore cancelled events upon fetch I OK if not too many cancellations 3.7 2.9 4.2 3.1 I See code on website "e1" "e2" "e3" "e4" "e5" "e6" "e7" 7 / 9

Hybrid Data Structures Bucket System I Event time “hashes” to a bucket ... 1-10 10-20 20-30 80-90 overflow I Recycle buckets when they become empty 1.3 12.6 24.0 87.2 230.1 Henriksen’s algorithm I Used in many 5.8 17.7 28.2 early commercial systems I Combines binary search tree 7.2 19.3 with doubly-linked list I Can have bad worst-case behavior 8 / 9

Hybrid Data Structures, Continued Lazy Queue [Ronngren et al. 1991] I Three parts: I Near Future (NF): a sorted linked list I Far Future (FF): an unsorted bucket system I Very Far Future (VFF): an unsorted linked list I Sorting only happens when FF NF FF VFF bucket is moved to NF 0-1 1-2 2-3 3-4 4-5 5-6 > 6 I Occasional adaptive resizing of # and length of buckets I Dominates most other event list schemes for > 50 events sorted unsorted 9 / 9