The arrival rate at the second server in a two stage serial queuing system is Service rate of server 1 Same as arrival rate at server 1 Minimum of service rate and arrival rate at server 1 Cannot be determined
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The arrival rate at the second server in a two stage serial queuing system is
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- The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of the canteen arrive at an average of 50 an hour. Suppose that management wants to evaluate the desirability of opening a second order-processing station so that two customers can be served simultaneously. Assume a single waiting line with the first customer in line moving to the first available server. a. What is the average arrival time in minutes of customers? b. What is the average service time in minutes of the canteen? c. What is the probability that the canteen has a customer?For the Burger Dome single-channel waiting line, assume that the arrival rate is 1 customer per minute and the mean service rate is 1.25 customers per minute. Compute the following operating characteristics for this queuing system: P0, Lq, L, Wq, and W.
- Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…CWD Business systems maintains a successful Telecom sales department for Top up call creditin which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phonecalls to the department are answered automatically by an answering machine and asked to wait.As soon as the clerk is free, the party that has waited the longest is transferred and answered first.Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an averageof 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential.The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 perhour of customer time spent waiting for the clerk to take an order. Part B CWD is considering adding a second clerk to take calls. The store would pay that person thesame $15 per hour.Using appropriate formula for the multiple channel model, answer the following questions. a. What is the probability that no customers are…Premium control has a three machine process; the reliability ratings for the machines in the process are 0.7, 0.8, and 0.9. Each machine in the process is backed up by a redundant machine which has a reliability of 0.9. The increase in system reliability due to the redundancy is -----%?
- Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.04 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.4 machines per hour. Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours Each employee…Determine the mean waiting time W for an M/M/2 system when lambda = 2 and μ = 1.2. Compare this with the mean waiting time in an M/M/1 system whose arrival rate is lambda = 1 and service rate is μ = 1.2. Since the arrival rate per server is the same in both cases and service times don’t vary, should the wait times be the same in both cases?A grocery is supplied from 3 suppliers Fi(i = 1,2,3) who have: F1 of 5 trucks, F2 of 4 trucks and F3 of 6 trucks. The grocery is planned for a period of time, 12 trucks of goods. The transport from each supplier costs 40 monetary unitsfor F1, 60 monetary units for F2, respectively 50 monetary units for F3. Establish a supply schedule from the three suppliers so that the total cost of transport is as low as possible(minim cost). Observation: This is a linear program problem, i need only the mathematical model without solutions for the system, i only need those inequations.
- A local retailer anticipates an annual demand 16000 units of a product. The retailers] allows shortages for that product, and these shortages are backordered at a rate of 2 OMR per unit backordered. The cost of ordering is 300 OMR, whereas, the annual holding cost is 1 OMR per unit. The retailer operates 300 days per year. What is the optimal order size in units? Round-up to the nearest integerThe addition of bran to the porridge has been reported in increasing the sales to the hospitals by the Sales and Marketing Manager, Pakistan region of Quaker Chemicals Pvt Ltd. Several different bran preparations are available, and the Manager wants to test the efficiency of two of them, since favorable claims have been made for each by the clinicians. Among the consequences of administering bran that requires testing is the transit time through the alimentary canal in human body. Alimentary canal is a system within humans and other animals which takes in food, digests it to extract and absorb energy and nutrients, and expels the remaining waste. The clinicians and the Sales Manager wonder whether transit time would be shorter if bran is given in the same dosage in three meals during the day (Treatment 1) or in one meal (Treatment 2) to the same patients. A random sample of patients with disease of comparable severity and aged 20-44 is chosen and the two treatments are administered on…A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below; No of Customers Commercial dist branch (time) Residential area branch (time) 1 – 5 3 3 6 - 10 5 6 11 - 15 8 5 16 – 20 8 3 21 - 25 4 2 Required Which of the branches has a relatively better mean waiting time? Which shop can be surer of meeting the mean waiting time at the two branches? Assuming…