ADM 3301 Lecture Notes - Lecture 12: Poisson Distribution, Markov Chain, Exponential Distribution

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lilachippopotamus32

1 Aug 2018

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> possible to have models where the service rate is an adjustable number where faster service times can be bought . > the most common distribution for modelling service times is the exponential distribution. Long right tail representing the fact that most clients don"t take too long but occasionally there is a client who takes a really long time! > memoryless (i. e. the expected length of service does not change if you have already received service for x time units) > also represents inter-arrival times if arrivals follow a poisson distribution. > while exponential is often a good representation of service time, it is not always the case (i. e. surgical times more likely to follow a log- normal) > the poisson and exponential distributions are directly related as if the number arrivals follows a poisson distribution, then the time between successive arrivals follows an exponential distribution. This process is referred to as markovian process.

Related Questions

A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered:

System A: A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes.

System B: A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes.

System C: A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money for customers arriving at the window. The average service time for this alternative is 2 minutes for each server.

The following cost information is available.

Customer waiting time is valued at $25 per hour to reflect the fact that waiting time is costly to the fast-food business.

The cost of each employee is $6.50 per hour.

To account for equipment and space, an additional cost of $20 per hour is attributable to each server.

What is the lowest-cost design for the fast-food business? If required, round your answers to two decimal places.

	Total Cost
System A	$
System B	$
System C	$

System A, B, or C is the most economical.

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ADM 3301 Lecture Notes - Lecture 12: Poisson Distribution, Markov Chain, Exponential Distribution

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