1. There is a Poisson queuing system with the average customer arrival rate of 3 customersper half of hour. This system starts working at 9:0 am. For this system, calculates:iv. The least number of servers needed in the system to ensure that each server would bebusy in 70 percent of time at most.

Queueing systems are basic mathematical models used to explain traffic bottlenecks. In general, a…

Answered: There is a Poisson queuing system with…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 1:00 p.m. and 2:00 p.m. on any given day?▪ How likely is it that once a truck is in position at a well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪…
Josh’s Hot Dogs is a one-person hot dog stand, and normally gets about 14 customers per hour. Assuming that Josh can serve one customer in about 3 minutes. What impact does this have on the queuing characteristics? Specifically, the following questions:a. Mean number of customer in the queue b. Mean number of customer in the system: c. Mean waiting time in the queue:d. Mean waiting time in the system:e. Utilization factor for the system:f. Probability of more than 1 customer in the system at any given time.g. Do you think he has an acceptable queuing system?
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1
Give and explain briefly that in what kinds of situations is queuing analysis is most appropriate.
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service rate of 15 customers per hour. The average length of time customers will spend in the system is: O a. 2.667 minutes O b. 0.1111 minutes O c. 6.667 minutes O d. 0.04444 minutes
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Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) serves 5 customer/hr, on average. Assume an M/M/s queue system. Prof. Karen calculates the operational cost of each server as $20/hr, and assumes a cost of waiting in the SYSTEM as $25/hr per customer. What is the optimal number of service windows to minimize total cost?

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There is a Poisson queuing system with the average customer arrival rate of 3 cus per half of hour. This system starts working at 9:0 am. For this system, calculates: iv. The least number of servers needed in the system to ensure that each server wo busy in 70 percent of time at most.