BU275 Study Guide - Final Guide: Risk-Seeking, Poisson Point Process, Posterior Probability
BU-275 Final Reie
Queues
• Customers arrive at a movie theatre according to a Poisson Process at a rate of 40 per hour.
There are 4 ticket booths, a queue forms in front of each, customers divide themselves evenly
and no jockeying. The service time of each teller is exponential with average 3 minutes, together
the booths can serve 80 people per hour.
o This is 4 M/M/1 Queues.
o The = System / number of queues. = 40/4 = 10 per hour
o The = 1/service tie = 1/3 =20 per hour
o No special restrictions
• Customers arrive to a shop with a single cashier according to a Poisson Process of 10 per hour.
Service time is exponential average of 2 minutes.
o This is 1 M/M/1 queue
o The =10/1=10 per hour
o The =1/2=30 per hour
o No special restrictions
o 2/81 chance of 2 people in line
• Customers arrive at a coffee shop, time between intervals is exponential average 10 minutes, 2
cashiers each has an exponential service time of 8 minutes. They are paid $12 per hour. There is
a cost of $0.25 per minute that each customer spends in store. If customers split evenly into 2
lines what is the cost per hour of the system?
o Cost of system = cost of service + cost of waiting = (#of servers)*($$per server
hour)+(cost per hour per customer in system)*(L)
o Or: Cost of system = cost of service + cost of waiting = (#of servers)*($$per server
hour)+(cost per hour per customer in line)*(Lq)
▪ We use first as we have cost per customer in system.
o =6/= per hour
o =1/8=7.5 per hour
o L=0.67
o Cost of being in system = ($0.25)*(60 mins)*(0.67)=$10.05
o There are 2 lines, so total cost = 2*(12+10.05)=44.10)
Bayesian Updating
• A potential site for a power plant has a small earthquake risk, estimated at 30% over the next 5
years. A geologist can issue a Report predicting safe or unsafe conditions. In the past, given
there was an earthquake, the report correctly predicted it 95% of the time. If there was no
earthquake, she was right 75% of the time. When the geologist issues a safe report, the
probability she is wrong is?
o These are conditional probabilities, so we need the posterior probability.
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Document Summary
Queues: customers arrive at a movie theatre according to a poisson process at a rate of 40 per hour. There are 4 ticket booths, a queue forms in front of each, customers divide themselves evenly and no jockeying. The service time of each teller is exponential with average 3 minutes, together the booths can serve 80 people per hour: this is 4 m/m/1 queues, the (cid:644)= system (cid:644)/ number of queues. = 40/4 = 10 per hour: the (cid:645) = 1/service tie = 1/3 =20 per hour, no special restrictions, customers arrive to a shop with a single cashier according to a poisson process of 10 per hour. There is a cost of sh. 25 per minute that each customer spends in store. Bayesian updating: a potential site for a power plant has a small earthquake risk, estimated at 30% over the next 5 years. A geologist can issue a report predicting (cid:862)safe(cid:863) or (cid:862)unsafe(cid:863) conditions.
