1. Customers arrive at a single-server queueing system according to a Poisson process at a mean rate of 30 perhour. If the server works continuously, the number of customers that can be served in an hour has a Poissondistribution with a mean of 50. Determine the proportion of time during which no one is waiting to be served.

The proportion of time during which nobody is waiting to be served refers to the fraction of time…

Answered: Customers arrive at a single-server…

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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A community is served by two identical companies providing taxi booking services. Each company owns two cabs, and both book rides at an average rate of eight per hour. The average duration of a ride is 12 minutes meaning each cab makes 5 rides per hour. Calls for booking arrive according to a Poisson distribution, and the rides made is exponential. The two companies have been bought by an investor and will be merged into one. Analyze the new investor's proposal. The following is the queueing model of each company before and after they merge: Company C A = ? rides booked/hr u = ? rides made/hr c = ? cabs Company A Company B A = 8 rides booked/hr µ = 5 rides made/hr 2 cabs A = 8 rides booked/hr µ = 5 rides made/hr = 2 cabs %3D %3D %3D C = с 3 %3D
In a queueing system, customers arrive once every 3 hours (standard devlation = 4) and services take 2 hours (standard deviation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customers
In an M/MA queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. (Round your answers to 3 decimal places.) a. What is the probability that the server will be idle? Probability b. What is the probability of having exactly 4 customers in the system? Probability c. What is the probability of having 3 or fewer customers in the system? Probability
Suppose you’re designing a toll bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 400 per hour. You will have five toll booths, which can each process cars at a rate of 120 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution with a mean rate of 400 units per period. Assume car processing times are exponentially distributed with a mean service rate of 120 units per period. 1. What is the probability that two channels are busy and no units are waiting in the queue? 2. What is the steady-state average length of the queue (waiting line)? 3. What is the mean number of units in the system (queue and service)?
A call centre operates with two customer service representatives. Customers call the centre according to a Poisson process with an average rate of 10 calls per hour. The service times follow an exponential distribution with a mean service rate of 6 calls per hour per representative. The goal is to analyse the performance of this queuing system and determine key metrics.
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.0 per minute. In serving themselves, customers take about 25 seconds, exponentially distributed. (a) How long would you expect it to take to get a cup of coffee, including waiting time? (b) If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 25 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?
Consider a system with Poisson distributed arrival rate with average of 10 clients per day. The service time is exponentially distributed with 8 clients per day. If the cost for operating each server is $20 per day and the cost of holding a client in the system is $200 per day, What is the total cost of operating with 5 servers? Answer is $350.65 please explain.
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?
In improving services to consumers, Limited Company Prima conducted a study of the queue time spent by consumers during the payment process with one available payment service.The average arrival of consumers in 1 hour is 8 consumers, while every hour the number of customers who can be served is 10 consumers. Count: a. The average length of time the customer is in the storeb. Average number of consumers who are being servedc. If the waiter fee is 500 and the subscription fee is waiting for 100, calculate the hourly amount
Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
A firm is engaged in both shipping and receiving activities. The management is always interested in improving the efficiency of new innovations in loading and unloading procedures. The arrival distribution of trucks is found to be Poisson with arrival rate of 3 trucks per The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine (i) expected number of trucks in the queue, hour. (ii) expected waiting time of the truck in the queue, (iii) probability that the loading and unloading dock and workers will be idle, (iv) what reductions in waiting time are possible if loading and unloading is standardised?

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