Consider a single server queuing system. The system starts at time t=0. The arrival time of customers is: 0.8, 1.4, 2.7, 3.2, 3.8, 8.0, 8.6, 9.0, 9.2, and 9.8. The departure times are: 2.2, 4.0, 5.0, 6.2, and 10.0. Time is in minutes. The first in first out queuing discipline is followed. Simulate this system for six clients and estimate:i) The average delay in the waiting line ii) The average number of clients in the waiting line at any time t iii) The expected utilization of server.

Consider a business process in which each order that arrives is split into two jobs that are performed in parallel and are then rejoined before leaving the system. Assume no variance in inter-arrival times nor in process times for each task. Each station (depicted by a rectangle) contains one or more identical parallel servers (depicted by circles). Each server is independent of all others and can work on one job at at a time. Process times for individual servers at station A are 5 minutes. Servers at stations B and C have process times of 3 and 6 minutes respectively. Consider the system with one server per station. What is this system's capacity? What is the cycle time for each order through the entire process flow?

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 38 calls per hour. The service rate per line is 23 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…

Suppose i am going to build a digital model for all 4 different products coming to awarehouse. All products first move to a temporary waiting area and then to inspectionmachines. There are 4 inspection machines to process each product respectively. Afterinspection, all products must move to next station for scanning before they are finallytransported to 4 racks.Products arrives exponentially with an average of 12 seconds. Processing times of inspectionmachines ars exponentially distributed with an average 6 seconds. Scanning time is fixed 4seconds.Simulation time is 50000s, Queue capacity is 10000.Suppose i need to redesign this process. How would it be possible to improve this system.Maybe identify the bottleneck by output analysis and propose improvement solution byadding additional object(s) or new automated resource to the original model will be possible?

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…

The manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?

Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?

Bacala Software Systems operates a technical support center for its software customers. If customers have installation or user problems with Bacala software products, they may telephone the technical support center and obtain free consultation. Currently, Bacala operates its support center with one consultant. If the consultant is busywhen a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and the consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution with an arrival rate of five calls per hour.On average, it takes 7.5 minutes for a consultant to answer a customer’s questions. The service time follows an exponential probability distribution. (Please Answer a-c) thank you!  a. What is the service rate in terms of customers per hour?b. What is the probability that no customers are in the system and the…

In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle?       What is the probability of having exactly 4 customers in the system?       What is the probability of having 4 or fewer customers in the system?

The VBO grocery store has a checkout counter with a full-time cashier. Customers arrive randomly with an average rate of 20 per hour. The distribution of service time is exponential with an average of 2 minutes. Occasionally, this situation causes a long queue and customer complaints. Since there is no room for another cashier, the manager plans to hire another person to help pack the groceries and reduce the expected service time to 1.5 minutes, still with exponential distribution.  The manager wants the percentage of time when there are more than 2 customers at the cash register to be less than 25%. He also wants no more than 5% of customers to have to wait 5 minutes or more before starting service or 7 minutes or more before finishing service.  a) Use the formulas from the M/M/1 model to calculate L, Lq, W and Wq, π0, π1 and π2 of the current transaction. What is the probability that there are more than 2 customers at the cash register?   (b) Repeat (a) for the helper alternative.