A take-out fast food restaurant located in a busy downtown area has one window open from 11:00am to 11:00pm each day. It is found that every 10 minutes (in average), there is a customer coming to the restaurant. The average time to serve a customer (including time to place order, time to get food ready and time to pay the bill) is 4 minutes. It is also observed that both arrival and service processes follow Poison distributions. Use the standard queuing theory models discussed in class to evaluate the situation of the restaurant by calculating: 5.1) the estimated time that the service window is busy serving customers in the 12 hours each day 5.2) the expected time a customer will wait to get served after he/she arrives at the restaurant 5.3) the expected time a customer will spend at the restaurant (including waiting time and the time of being served) after he/she arrives at the restaurant 5.4) the estimated time that there are 2 or more customers in the restaurant in the 12 hours each day You may use the following equations in answering this question. System utilization: p =4, where A is customer arrival rate and µ is the service rate. Expected time in queue: T, %3D µ(µ-A) 1 Expected time in system Ts = (µ-2) n Probability that there are n customers in the system: P(n) = P(0) × (A)" = (1– 4) × (4)"
A take-out fast food restaurant located in a busy downtown area has one window open from 11:00am to 11:00pm each day. It is found that every 10 minutes (in average), there is a customer coming to the restaurant. The average time to serve a customer (including time to place order, time to get food ready and time to pay the bill) is 4 minutes. It is also observed that both arrival and service processes follow Poison distributions. Use the standard queuing theory models discussed in class to evaluate the situation of the restaurant by calculating: 5.1) the estimated time that the service window is busy serving customers in the 12 hours each day 5.2) the expected time a customer will wait to get served after he/she arrives at the restaurant 5.3) the expected time a customer will spend at the restaurant (including waiting time and the time of being served) after he/she arrives at the restaurant 5.4) the estimated time that there are 2 or more customers in the restaurant in the 12 hours each day You may use the following equations in answering this question. System utilization: p =4, where A is customer arrival rate and µ is the service rate. Expected time in queue: T, %3D µ(µ-A) 1 Expected time in system Ts = (µ-2) n Probability that there are n customers in the system: P(n) = P(0) × (A)" = (1– 4) × (4)"
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:A take-out fast food restaurant located in a busy downtown area has one window open from 11:00am to 11:00pm each
day. It is found that every 10 minutes (in average), there is a customer coming to the restaurant. The average time to
serve a customer (including time to place order, time to get food ready and time to pay the bill) is 4 minutes. It is also
observed that both arrival and service processes follow Poison distributions. Use the standard queuing theory models
discussed in class to evaluate the situation of the restaurant by calculating:
5.1) the estimated time that the service window is busy serving customers in the 12 hours each day
5.2) the expected time a customer will wait to get served after he/she arrives at the restaurant
5.3) the expected time a customer will spend at the restaurant (including waiting time and the time of being served)
after he/she arrives at the restaurant
5.4) the estimated time that there are 2 or more customers in the restaurant in the 12 hours each day
You may use the following equations in answering this question.
System utilization: p =4, where A is customer arrival rate and u is the service rate.
Expected time in queue: Ta
Expected time in system T, =
(H-2)
() = (1 - 4) × ()"
n
Probability that there are n customers in the system: P(n) = P(0) x
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