1. Queues

2. Examples of Queue Problems Post Office Post Office (Each counter with all services v Different counters for different services) T-Mobile Customer Service T-Mobile Customer Service (How many operators to employ and when ?) Airport Airport (What is the chance that the aircraft will have to wait before landing ?)

3. Basic Language of Queues Arrivals (Probability distribution) Arrivals (Probability distribution) Service mechanism Service mechanism Queue discipline Queue discipline Service time variability Service time variability Service discipline Service discipline

4. Variability of arrivals Number of arrivals changes in each time period. Number of arrivals changes in each time period. Assume 2 arrivals cannot occur simultaneously. Assume 2 arrivals cannot occur simultaneously. Assume infinite queue potential Assume infinite queue potential

5. Service mechanism Usually controlled Usually controlled Single channel or multi-channel Single channel or multi-channel (eg. Toll booths, ASDA etc) Multiple channels may be in series Multiple channels may be in series

6. Queue discipline Jockeying Jockeying Balking Balking FIFO FIFO LIFO LIFO Random Random Queue jumping Queue jumping

7. Service Time variability Measured by a frequency distribution Measured by a frequency distribution Might be affected by numbers in the queue Might be affected by numbers in the queue

8. Service discipline Fixed batches Fixed batches (eg. Tour of mine shaft) Fish shop Fish shop (eg. Battered cod is just cookin’)

9. Which is best ? (a) 3 channels in parallel each operating at mean service rate = 10 per hour; (a) 3 channels in parallel each operating at mean service rate = 10 per hour; OR OR (b) 1 channel with a mean service rate of 30 per hour ? (b) 1 channel with a mean service rate of 30 per hour ?

10. The answer is … (b) By 2.6 minutes per customer ! OK.. Now look at the Excel worksheet. OK.. Now look at the Excel worksheet.