What happens if two single-channel systems have the same mean arrival and service rates, but the service time is constant in one and exponential in the other?

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours

A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 37 calls per hour. The service rate per line is 24 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0)=P(1)=P(2)=P(3)= (b) What is the probability that an agent will be denied access to the…

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%…

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place.   Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number.   Calculate the average time in the system. Note: Round your answer to the nearest whole number.   Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…

Which of the service gaps do you consider to be most critical, and why?

For a single-server queue of 10 customers whose arrival and service time is given below in the table. Complete the below given table.   Customer Arrival Time ti Inter Arrival Time Ai=ti—ti-1   Service Begins (Sb) Delay Time (Di) Service Time (Si) Calculate Ci=ti+Di+Si 1 7:00   7:02   6   2 7:08   7:12   4   3 7:11   7:16   1   4 7:13   7:19   5   5 7:18   7:25   10   6 7:36   7:39   2   7 7:40   7:44   3   8 7:45   7:48   3   9 7:49   7:52   4   10 7:55   7:57   3     Find the average service time and average delay time. Average Service Time= Average Delay Time=