Workers come to tool store room to enquire about special tools (required by them) for accomplishing a particularproject assigned to them. The average time between two arrivals is 60 seconds and the arivals are assumed to bein Poisson distribution. The average service time (of the tool room attendant) is 40 seconds.Determine:(1) average queue length,(i) average length of non-empty queues,(ii) average number of workers in system including the worker being attended(iv) mean waiting time of an arrival,(v) average waiting time of an arrival who waits.

Given, Arrival Rate λ = 6060 per second = 1 per minute Service Rate µ = 6040 per second =1.5 per…

Answered: Workers come to tool store room to…

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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At a fashion retailer, there are 3 cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It has been estimated that the arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 16 minutes. Suppose that customers form a single line. What is the average length of the line (i.e., average number of customers in the waiting line)? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
Why do queues arise at a service facility even though there is more than enough capacity to meet regular demand in the long run?
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.
Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.
A. Know some of the basic queue performance measure B. Identify the relationships between queues and some statistical distribution
Assume that at a bank teller window the customers arrive in their cars at the average rate of twenty per hour according to a Poisson distribution. Assume also that the bank teller spends an average of two minutes per customer to complete a service, and the service time is exponentially distributed. Customers, who arrive from an infinite population, are served on a first-come-first-served basis, and there is no limit to possible queue length.a. What is the expected waiting time in the system per customer?b. What is the mean number of customers waiting in the system?c. What is the probability of zero customers in the system?d. What value is the traffic intensity?
Please do not give solution in image format thanku
[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
In an M/MA queueing system, the arrival rate is 5 customers per hour and the service rate is 9 customers per hour. If the service process is automated (resulting in no varlation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) a. What is the utilization? Ubization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected walting time (in hours) for the system (W? Waiting timetin nours)
Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. Assume that service times are exponentially distributed and that the queuing system model is (M/M/1):(GD/infinity/infinity). Does this queuing system have a steady state? It cannot be determined. Yes none of the other choices No
Please do not give solution in image formate thanku. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Required: (g) Assume that the information desk employee earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8

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