14. A small town's hospital wanted to an analysis about the ambulance number that they own/needto own. Requests for ambulance is 0,45 per hour and tend to follow Poisson-distribution. Traveland assistance time averages two hours per call. There is no assumption regarding the distributionof service time.a. What are the arrival and service ratesb.Compute the average number of customers being served at any timec. Calculate the system utilization for total number of server values of M=1,2 and 3d. Suppose someone made a day long observation and concluded that the average queue lengthis 1,7 requests. Then please calculate the average number of people in the system.

To analyze the number of ambulances needed, we can use queuing theory.

Answered: a. What are the arrival and service…

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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(Requires the use of a spreadsheet or LINGO) USAirlines receives an average of 500 calls per hour fromcustomers who want to make a reservation (time betweencalls follows an exponential distribution). It takes an averageof 3 minutes to handle each call. Each customer who buys a ticket contributes $100 to US Airlines profit. It costs $15per hour to staff a telephone line. Any customer who receivesa busy signal will purchase a ticket on another airline. Howmany telephone lines should US Airlines have?
Consider an M/G/1/GD/∞/∞ queuing system in which anaverage of 10 arrivals occur each hour. Suppose that eachcustomer’s service time follows an Erlang distribution, withrate parameter 1 customer per minute and shape parameter 4.a Find the expected number of customers waiting inline.b Find the expected time that a customer will spend inthe system.c What fraction of the time will the server be idle?
20. A small bank is trying to determine the number of tellersto employ. The total cost of employing a teller is $100per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day atthe bank, and both service times and interarrival times areexponentially distributed. If the delay cost per customerday is $200, how many tellers should the bank hire?
In a M/M/1 queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate). What will be the resulting performance measurements? (Round your ansers to 3 decimal places) a. What is the expected number of customers in the queue (Lq)? b. What is the expected waiting time (in hours) in the queue (Wq)?
A server operates with 80 % utilization. Coefficient of variation of service process is 0.5. Coefficient of variation of arrival process is 0.9. Average processing fime is 3 minutes. What is the average time a customer spends in the system using the single server queueing model 7 Show all formulas used, calculations and results.
Describe at least 4 operating characteristics you can determine by performing queue analysis. What is the purpose of doing queue analysis to the business owner, i.e., what are possible actions (at least 2) that a business owner or manager might want to take, once the operating characteristics are understood?
4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?
Answer the following questions. Answers are listed at the end of this section.1. The queuing models assume that customers are served in what order?2. Consider two identical queuing systems except for the service time distribution. In the first system, the service time is random and Poisson distributed. The service time is constant in the second system. How would the waiting time differ in the two systems?3. What is the average utilization of the servers in a system that has three servers? On average, 15 customers arrive every 15 minutes. It takes a server exactly three minutes to wait on each customer.4. What is the expected waiting time for the system described in question 3?5. Firms that desire high service levels where customers have short wait times should target server utilization levels at no more than this percentage.
1.)The arrival rate is the rate of arrivals to the service facility all of these rate items arrive at the server after being in the queue time between arrivals to the service facility 2.) what is "queue discipline"?
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day (assume Poisson). Use Table 1. a. Determine the average number of customers awaiting repairs. (Round your answer to 2 decimal places.) Average number of customers
Twenty-one customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 2 minutes to fill each order (following a negative exponential distribution). The Waiting Line Table is provided below and also we know that ... a) What is the average number of customers in the queue? Using the table, the average number of customers in the queue is ______ customers (round your response to four decimalplaces). b) How long will a person wait in line on average? The average time a person spends in the queue is ______ minutes(round your response to two decimal places). c) If Andy's wife joins him in serving meals (at the same speed as Andy), how will your answers to parts a and bchange? Using the table, the new average number of customers in the queue is _________ customers (round your response to four decimal places). The new average time a person spends in the…

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