The Joy of Queueing Dr. Mark P. Van Oyen This is a somewhat lighthearted introduction to queues for those new to the mo

1. The Joy of Queueing Dr. Mark P. Van Oyen This is a somewhat lighthearted introduction to queues for those new to the modeling of queues. Filename: 574queue-lec-A.ppt

2. Queuing Systems • Queue is a line of waiting customers who require service from one or more servers (service providers represent service capacity - machines, tools, workers, etc.). • Queueing system = waiting room + customers + server + workstations Arrivals QueueServer(s)Departures

3. How many examples of queues can you think of? (REAL WORLD and at LUC) in line for • Lunch/dinner at cafeteria • Video rental • Banking • Buying groceries • Complex • Service at sit -down restaurant • “Simple” … waiting • Amusement parks (network of queues) • Waiting for train/bus ride • Traffic congestion & waiting for traffic signals • ordering a Harley Davidson, then waiting for it to come.

4. OTHER QUEUES • Parts on an assembly line (with random arrival/production times) • Planes waiting to land/take off/load/unload • Rides waiting to load/unload at Disney World • Trucks/trains/ships waiting at loading docks • Orders waiting to be handled • Payments waiting to be mailed • 30% off sale at your favorite department store What country has the #1 practitioners of queueing?

5. Queueing Happens … But Why? • Queues form whenever current demand (temporarily) exceeds existing capacity to serve. • Variability of Demand: patterns are irregular or random (measure: Std. Dev of job interarrival times) • Service times vary among “customers” or “jobs” (measure: Std. Dev of job service times) • Managers try to strike a balance between efficiently utilizing resources (which comes at the price of high WIP and long cycle-times) and keeping customer satisfaction high (which usually requires lower utilization levels). • Waiting increases when the variability of arrival times and/or service times increases.

6. Who Cares About Queueing? • Service Operations • random customer arrivals • service time variability • Manufacturing/Production Systems • variability in machine processing times, routing • variability in customer demand • Can you think of a business which does not care about queueing? The government is not a business ;-)

7. Queueing Behaviors(Simulation adds analytical power for complex dynamics) • Waiting behaviors: • Balking. (That line is so long … I’m not even going there!) • Reneging. (I’ve been waiting so long, I think I will give up) • Jockeying. (I think I can move up, so switch lines) • Jockeying can make people mad • Balking (e.g. based upon an announced waiting length) can be better than misperception that ends in reneging.

8. Because of the diversity of Queueing Systems, we categorize them. The 5 most important factors: 1. The queue discipline(protocol or service order) • The size of the calling population(assume infinite customer base, but professor’s office hours don’t fit this model) 3.The arrival rate(frequency of customers arrivals) 4.The service rate(how fast customers are served) 5.The structure of the service facility (the number of queues,number of servers, & number of phases in sequence)

9. 1. The Queue Discipline(the order the customers are served) A. “First come, first served” FCFS or FIFO. This is the most common discipline. Customers are served in the order they come into the queue B. “Last come, first served”LCFS or LIFO. Here the last customer to get in line is served first (e.g. an elevator in which last on = first off . Also has batch service feature) C. Scheduled – arrivals/service scheduled (e.g. doctor’soffice)Why Schedule? Why not? D.Priority.Here customers are serviced by some priority system (e.g. hospitals or universities with tiered registration) E. Random. Customers are serviced at random independent of their arrival time (e.g. model of riding a bus)

10. 3. The Arrival Rate (Frequency) • Average number of customers/jobs arriving to service facility during a unit of time • e.g., if 160 customers arrive in an 8 hour day, then the average arrival rate is 160/8 = 20 per hour • THIS is just a NUMBER. Need a distribution on interarrival time to get variability info. (this raises the need to use collected data to fit an appropriate distribution) • Mean interarrival time is RECIPROCAL of rate (analytical models refer to transition rates, while simulation conventions are parameterized by the mean, variance, and other param’s)

11. 4. The Service Rate • Service Rate = Average number of customers that can be served during a unit of time (at 100% utilization). • In general, we must define a service process, which may include correlations. • For simplicity, we often assume i.i.d. service times from a specified (general) distribution. • Cases include … • Fixed Rate: (e.g. exactly 15 per hour), which minimizes congestion • Random service distributions that vary with the size and type of transaction. • Our favorite: Memoryless - exponential(mean 1/) probability distribution.

12. 5. Structure of the Service Facility 3 Components The number of channels or queues (default =1) The number of servers (default =1) The number of phases in sequence (default =1) Examples: • 24 hour Bank Teller:1 queue, 1 server, 1 phase; • Disney World: queues, many servers, many phases. This leads to analytical models with routing structures that depend either on the customer type or the particular workstation at which service occurs.

13. departures arrivals Standard queue symbol GI/GI/1 queue is our general single-server queue model Examples of types of Queueing System Structures: • Single Queue - Single Server (e.g. a small gift shop with only one cashier)

14. Examples of types of Queueing System Structures: • Basic Model: Single Queue - Multiple Servers in Parallel (e.g. a bank, airport counter) • Complex: If customers belong to different classes and tellers differ in terms of the skills they posess, then this becomes an interesting problem!

15. Examples of types of Queueing System Structures: • Single Queue with Multiple Servers with phases in series (e.g. a large car wash)