A queuing system with a Poisson arrival rate and exponential service time has a single queue,...
A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer.
Answer the following questions. Show ALL formulas and calculations used in your response.
- The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain.
- How many additional servers are required to ensure the utilization is less than or equal to 50%? Explain.
- If the manager loses a server, what service time would be necessary to ensure that the queue length is not at risk of approaching infinity? Explain.
Instructions:
- Answers should include FULL explanations, including formulas
Homework Answers
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A queuing system with a Poisson arrival rate and exponential
service time has a single queue,...
3) A single server queuing system with an influence calling population and a first-come, first-serve queue...
3) A single server queuing system with an influence calling population and a first-come, first-serve queue discipline has the following arrival and service rates (poisson distributed): A=16 customers per hour U=24 customers per hour Determine PO, p3, L, Lq, W, Wq, and U
Consider the M/M/1/GD/∞/∞ queuing system where λ and μ are the arrival and server rate, respectively....
Consider the M/M/1/GD/∞/∞ queuing system where λ and μ are the arrival and server rate, respectively. Suppose customers arrive according to a rate given by λ = 12 customers per hour and that service time is exponential with a mean equal to 3 minutes. Suppose the arrival rate is increased by 20%. Determine the change in the average number of customers in the system and the average time a customer spends in the system.
For an infinite-source, single server system with an arrival rate of 15 customers per hour (Poisson)...
For an infinite-source, single server system with an arrival rate of 15 customers per hour (Poisson) and service time of 2 minutes per customer (exponential), the average number waiting in line to be served is: a. 0.1 b. 0.133 c. 0.50 d.0.250
QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour...
QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour per server and arrival ratei - 45 customers per hour, on the verge, how long in minutes) does a customer wait in line round off to 2 decimal digits) QUESTION 10 A small branch bank has two teller, one for deposits and one fow withdrawals Cistomers arrivent arch teller's window with an average rate of 20 customers per hour. The total customer anivartes per...
3. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate...
3. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service rate, what is the formula for the average utilization of the system? a) l / m b) l / (m-l) c) l2 / m(m-l) d) 1 / (m-l) e) l / m(m-l) 4. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service...
Consider the M/G/1 queue with FIFO service (see Homework 6) Assume that (1) the arrival rate...
Consider the M/G/1 queue with FIFO service (see Homework 6) Assume that (1) the arrival rate is 1 customer per minute, and (2) the service times are exponentially distributed with average service time 45 seconds. 07. Find the server utilization 88. Find the average value of the waiting time (in minutes). 9. Find the probability that an arriving customer will wait in the queue for at least 1 minute. 10. Find the probability that an arriving customer who finds the...
Consider a system with Poisson distributed arrival rate with average of 10 clients per day. The...
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?
Question 1 Simulate the operation of a first-in-first-out queuing system until time TE = 30 minutes,...
Question 1 Simulate the operation of a first-in-first-out queuing system until time TE = 30 minutes, using the interarrival and service-times given below (in minutes) in the given order. Interarrival times: 4, 3, 1, 1, 5, 7, 10 Service times: 4, 4, 6, 9, 8, 7, 4, 6 Given that the first arrival occurs at time t = 0, create a record of hand simulation (on the table given in the last page) using the event-scheduling algorithm and compute the...
For the following problems compute (a) utilization, (b) average time a customer waits in the queue,...
For the following problems compute (a) utilization, (b) average time a customer waits in the queue, (c) average number of customers waiting in the queue, (d) average number of customers in service, (e) the average time a customer spends in the system. Problem 1. An average of 10 cars per hour (with variance 4) arrives at a single-server drive-in teller. Assume that the average service time for each customer is 5.5 minutes (with variance 5). Problem 2. Customers arrive to...
A single server waiting line system has an arrival pattern characterized by a Poisson distribution with...
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3) A single server queuing system with an influence calling population and a first-come, first-serve queue discipline has the following arrival and service rates (poisson distributed): A=16 customers per hour U=24 customers per hour Determine PO, p3, L, Lq, W, Wq, and U
QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour per server and arrival ratei - 45 customers per hour, on the verge, how long in minutes) does a customer wait in line round off to 2 decimal digits) QUESTION 10 A small branch bank has two teller, one for deposits and one fow withdrawals Cistomers arrivent arch teller's window with an average rate of 20 customers per hour. The total customer anivartes per...
Consider the M/G/1 queue with FIFO service (see Homework 6) Assume that (1) the arrival rate is 1 customer per minute, and (2) the service times are exponentially distributed with average service time 45 seconds. 07. Find the server utilization 88. Find the average value of the waiting time (in minutes). 9. Find the probability that an arriving customer will wait in the queue for at least 1 minute. 10. Find the probability that an arriving customer who finds the...
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?
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