1 Analysis Of Queues For this session, the learning objectives are:  Learn the fundamental structure of a queueing system.  Learn what needs to be specified before a queueing system can be analyzed.  Learn the operating characteristics and applications of a “basic” queueing system.

2 FUNDAMENTAL STRUCTURE OF A QUEUEING SYSTEM  Customers from a Calling Population arrive from time to time at the Queueing System. We will use the term customer regardless of whether the arrivals are people or inanimate objects (e.g., failed machines).  The time between consecutive arrivals is called the Interarrival Time.  Arriving customers join a Queue (which may at some times be empty).  At certain times, a group of one or more customers is chosen from the queue for service according to some rule called the Service Discipline.  A Service Mechanism then performs the customer’s required service, after which the customer leaves the queueing system and rejoins the calling population.  The time required for a customer’s service is called the Service Time.

3 SPECIFICATONS FOR A QUEUEING SYSTEM 1. Size of Calling Population Infinite Finite 2. Probability Distribution Governing the Interarrival Times. 4. Unusual Customer Behavior Batch Arrivals Balking Reneging Jockeying 5. Service Discipline First-In, First-Out (FIFO) Last-In, First-Out (LIFO) Random Priority 6. Configuration of Service Facilities that Comprise the Service Mechanism 7. Number of Servers at Each Service Facility 8. Probability Distribution Governing the Service Times. 9. Unusual Server Behavior Failure Changing Service Rates Batch Processing 3. Queue Capacity Infinite Finite

4 OUR BASIC QUEUEING SYSTEM

5

6 COMMON APPLICATIONS OF OUR BASIC MODEL