A discouraging M/M/1 queue behaves as M/M/1 but with an arrival rate equal to l/(j+1), where j is the number of customers in the system. a) Find the probability of each state. b) What is the average n...
A discouraging M/M/1 queue behaves as M/M/1 but with an arrival rate equal to l/(j+1), where j is the number of customers in the system.
a) Find the probability of each state.
b) What is the average number of customers in the system?
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A discouraging M/M/1 queue behaves as M/M/1 but with an arrival rate equal to l/(j+1), where j is the number of customers in the system. a) Find the probability of each state. b) What is the average n...
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/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.
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...
1) Find the probability that there are no customers in the system, given that: (i) number...
1) Find the probability that there are no customers in the system, given that: (i) number of channels in parallel = 3 (ii) mean arrival rate = 24 per hour (iii) mean service rate of each channel = 10 per hour
The first has one server and no limit on the length of the queue. Customers arrive...
The first has one server and no limit on the length of the queue. Customers arrive according to a Poisson process with rate 1. The service time is exponentially distributed with rate uk. Ilk is proportional to the number of people in the system. That is, where k is the number of people in the system and u is a constant. Mk = ku a = 1.5 M = 1.6 Part 1 0.0/10.0 points (graded) Determine the steady-state probability 11...
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...
QUESTION 8 Oakland post office uses a multiple channel queue, where customers wait in a single...
QUESTION 8 Oakland post office uses a multiple channel queue, where customers wait in a single line for the first available window. The average service time is 1 minute per cust, and the arrival rate is 1.4 cust. per minute, and # of channels, S-2 True/False PO Probability zero customers in the system between 0.17 and 0.18 True False
What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers i...
What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service).
What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service).
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures....
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures. Customer Arrival Time Service Time (min) Time Customer Waits in Queue (min) Time Customer spends in System (min) Idle Time of Server (min) 04 0) Average Waiting Time (11) Probability of a customer to be waiting (i.e., number of waiting customers over total number of customers) (II) Probability of idle server (i.e., proportion of idle time over total running time) (iv) Average Service Time...
1. Consider the M/M/1 queue where the arrive rate is λ and the service rate is...
1. Consider the M/M/1 queue where the arrive rate is λ and the service rate is μ (a) Give conditions on and such that the stationary distribution exists (b) For the rest of this problem, assume the stationary distribution exists. Calculate the stationary distribution (c) What is the expected number of individuals in the system at a given time? (d) When a new customer arrives into the queue, how long would they be expected to wait until the leave the...
The first has one server and no limit on the length of the queue. Customers arrive according to a Poisson process with rate 1. The service time is exponentially distributed with rate uk. Ilk is proportional to the number of people in the system. That is, where k is the number of people in the system and u is a constant. Mk = ku a = 1.5 M = 1.6 Part 1 0.0/10.0 points (graded) Determine the steady-state probability 11...
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...
QUESTION 8 Oakland post office uses a multiple channel queue, where customers wait in a single line for the first available window. The average service time is 1 minute per cust, and the arrival rate is 1.4 cust. per minute, and # of channels, S-2 True/False PO Probability zero customers in the system between 0.17 and 0.18 True False
What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service).
What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service).
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures. Customer Arrival Time Service Time (min) Time Customer Waits in Queue (min) Time Customer spends in System (min) Idle Time of Server (min) 04 0) Average Waiting Time (11) Probability of a customer to be waiting (i.e., number of waiting customers over total number of customers) (II) Probability of idle server (i.e., proportion of idle time over total running time) (iv) Average Service Time...
1. Consider the M/M/1 queue where the arrive rate is λ and the service rate is μ (a) Give conditions on and such that the stationary distribution exists (b) For the rest of this problem, assume the stationary distribution exists. Calculate the stationary distribution (c) What is the expected number of individuals in the system at a given time? (d) When a new customer arrives into the queue, how long would they be expected to wait until the leave the...
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