1. 1 Ch 12 M/G/1 Priority Queues Hong-Shik Park KAIST Tel) +82 42 350 3464 Email) parkhs@kaist.ac.kr

2. 2 Contents  Introduction  Conservation laws  An approach for calculating average waiting time  Shortest job first priority queue

3. Introduction  Classification according to priority queueing discipline Some measures related to the relative arrival times for those customers in queue (FCFS, LCFS, ROS) Some measures of service time required (SJF, LJF) Some function of group membership (HOL system) 3 Priority 1 2 3

4. Introduction  Model Customers from priority group p arrive in a Poisson process with rate p Each customer from group p has service time dist B p (x) and mean bp Class (group) 1 the highest priority and class P is the lowest priority Non-preemptive Preemptive: whenever higher priority customer appears in queue, a customer in service is ejected from service and returns to queue Preemptive resume: when re-service after preemption, start from the previous service finish time Preemptive repeat  Without resampling: use previously determined service time  With sampling: define new service time 4

5. Introduction 5

6. Conservation Laws 6

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8. An Approach for Calculating Average Waiting Time  A customer’s waiting time is decomposed into 3 parts 1) Any delay due to the customer found in service upon arrival 2) Any delay due to customers he finds in the queue upon arrival 3) Any delay due to customers who arrive after he does 8

9. An Approach for Calculating Average Waiting Time 9

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11. An Approach for Calculating Average Waiting Time 11

12. Shortest Job First Priority Queue 12 include x

13. Shortest Job First Priority Queue 13

14. Longest Job First Priority Queue 14