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Estimate the number of hours that the staff at the clinic are busy in a 12 hour time period Estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives. Estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/sh There is a seat in the clinic for the patient/person to sit down when he/she is treated. The clinic decided th

Estimate the number of hours that the staff at the clinic are busy in a 12 hour time period Estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives. Estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/sh There is a seat in the clinic for the patient/person to sit down when he/she is treated. The clinic decided th

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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A Covid-19 vaccine clinic in downtown area of a large city opens 24 hours a day and residents from all over the city may come to the clinic for service. Assume that the arrival process follows Poisson distribution with an average of 5 arrivals per hour. The average time required to give the vaccine is 8 minutes and the service time follows exponential distribution. Use the standard single channel single stage queuing model introduced in class and equations given below to calculate corresponding values in answering the following questions. 1) Estimate the number of hours that the staff at the clinic are busy in a 12 hour time period 2) Estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives. 3) Estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/she arrives. 4) There is a seat in the clinic for the patient/person to sit down when he/she is treated. The clinic decided that at least 75% of the time that a patient/person waiting to be served should have a seat and prepared 2 chairs in the waiting area. Use given information and formula to estimate if these 2 chairs in the waiting area are enough to meet this 75% target. Note that the formula of P(n) given below is to calculate the probability that there are n customers in the system including the one being served and those waiting. Formulas for single channel single stage queuing model 1: Arrival rate (number of customers arriving per unit time) u: Service rate (number of customers served per unit time) p = : Server Utilization Ta μ(μ-λ). Mean waiting time in queue 1 Ts (H-A) : Mean time in system (including service time) P(n) = P(0) (4)" =(1-4)()": Probability that there are n customers in system
Transcribed Image Text:A Covid-19 vaccine clinic in downtown area of a large city opens 24 hours a day and residents from all over the city may come to the clinic for service. Assume that the arrival process follows Poisson distribution with an average of 5 arrivals per hour. The average time required to give the vaccine is 8 minutes and the service time follows exponential distribution. Use the standard single channel single stage queuing model introduced in class and equations given below to calculate corresponding values in answering the following questions. 1) Estimate the number of hours that the staff at the clinic are busy in a 12 hour time period 2) Estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives. 3) Estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/she arrives. 4) There is a seat in the clinic for the patient/person to sit down when he/she is treated. The clinic decided that at least 75% of the time that a patient/person waiting to be served should have a seat and prepared 2 chairs in the waiting area. Use given information and formula to estimate if these 2 chairs in the waiting area are enough to meet this 75% target. Note that the formula of P(n) given below is to calculate the probability that there are n customers in the system including the one being served and those waiting. Formulas for single channel single stage queuing model 1: Arrival rate (number of customers arriving per unit time) u: Service rate (number of customers served per unit time) p = : Server Utilization Ta μ(μ-λ). Mean waiting time in queue 1 Ts (H-A) : Mean time in system (including service time) P(n) = P(0) (4)" =(1-4)()": Probability that there are n customers in system
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