ABC minorleaguesoccerteamhasoneboxofficeclerk.Onaverage,ticketscanbesoldto8customersperminute.Fornormalgames,customersarriveat therateof 5perminute.AssumearrivalsfollowthePoissondistributionandservicetimes followtheexponentialdistribution.

a.Whatistheaveragenumberofcustomers waitinginline?

b.Whatistheaveragetimeacustomerspendsinthewaitingline?

c.Whatistheaveragenumberofcustomersinthesystem?

d.Whatisacustomer's averagetimeinthesystem?

e.Whatistheprobabilitythatsomeonewillbebuyingticketswhenanarrivaloccurs?

The team isplayingintheleagueplayoffsandanticipatesmorefans,estimatingthatthearrivalratewillincreaseto12perminute.Outputissuppliedfora2-cashieranda3-cashiersystem.

NumberofChannels

2

3

ArrivalRate

12

12

ServiceRate

8

8

ProbabilityofNoUnitsinSystem

.1429

.2105

AverageWaitingTime

.1607

.0197

AverageTimeinSystem

.2857

.1447

AverageNumberWaiting

1.9286

.2368

AverageNumberinSystem

3.4286

1.7368

ProbabilityofWaiting

.6429

.2368

Probabilityof7inSystem

.0381

.0074

f.The stadium has space for 6 customers to wait indoors to buy tickets. Which of the two systems shown above will be better, and why?

g.Which system do you advise them to use in the new situation, overall: 1-, 2-, or 3-cashier? Justify your answer.