Chapter 13, Problem 17QP

Consider a Poisson queue with the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and pn = for n = 3,4,5, ... . What is the minimum number of stools that would accommodate all customers in the system at least 75% of the time in steady state? 3 stools O 2 stools none of the other choices O 1 stool

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?

(Random variables) Prove that the mean and standard deviation of the exponential distribution are equal (Queueing Theory) The time between failures of the kencore refridgerator is known to be exponential with mean values 9000 hours (about 1 year of operation), and the company issues a 1 year warranty on the refridgerator. what are the chances that the breakdown repair will be covered by the warranty?

An M/M/1 queueing system has that customers arrive to it at a rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an exponential distribution with parameter 5 per hour. This question will ask you to evaluate two options for designing the server in the system. Both options for the single server provide the same service for the customers in the queueing system but they cost different amounts to implement. In addition, the total costs of the queuing system are the implementation costs plus the customer costs. Currently, the customer costs are $100 per hour per customer in the queueing system. In comparing these options, it costs us $100 per hour per customer in the queueing system. (a) The first option for the server is one that has a service time that follows an exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this system. (b) The second option for the server is one that has a service time that follows an…

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

The QRS Trucking Services, has one warehouse servicing its 4 clients within the area. The warehouse hasonly one loading harbor with 3 service crews. The manager has observed that there are certain timeswherein their delivery vans are waiting in the harbor to be loaded. Also, there are instances whereintheir three service crews are idle. Thinking about the situation of their business , the manager noticedthat it follows the Single-Channel Queueing Model.Analyzing the record book, he noticed that the customers’ arrival rate is 3 delivery vans per hour, and onthe average service rate is 5 delivery vans per hour. What advise can you give to the manager about theimplication of adding another service crew, or even two or more crews to increase and improve theservice rate of his loading harbor?If the manager adds one or more service crew(s), the loading harbor can still be considered as a single-channel system, because only one delivery truck ( the customer) can be served at any one time.…

I need assitance with solving this problem 9. I made numerous attempts to solve. however I am still having issues. Please provide a step by step explanation so, I can use it as notes for future reference. Respectfully thank you

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 35 calls per hour. The service rate per line is 19 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 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 29 calls per hour. The service rate per line is 19 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…