Homework Answers
When you arrive the system you will have to wait for getting the service as two others are taking the service in server 1 and 2. So his expected time to get service includes his waiting time in the system for getting the first service + mean service time in server 1+mean service time in server 2
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Problem 3. The first problem on Mastery VI, version 1 had a certain system where customers...
Problem 3 Consider a single-server queueing system that can hold a maximum of two customers exclu...
Problem 3 Consider a single-server queueing system that can hold a maximum of two customers excluding those being served. The server serves customers only in batches of two, and the service time (for a batch) has an exponential distribution with a mean of 1 unit of time. Thus if the server is idle and there is only one customer in the system, then the server must wait for another arrival before beginning service. The customers arrive according to a Poisson...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, ...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
2. [3] Suppose you arrive to a service system with three...
2. (3) Suppose you arrive to a service system with three parallel servers. All servers are basy, ...
2. (3) Suppose you arrive to a service system with three parallel servers. All servers are basy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates μ1,P2, and μ3, what is the expected time you will spend in the system?
2. (3) Suppose you arrive to a service system with three parallel...
Consider an n server system where the service times of server i are exponentially distributed with...
Consider an n server system where the service times of server i are exponentially distributed with rate μi, i = 1,..., n. Suppose customers arrive in accordance with a Poisson process with rate λ, and that an arrival who finds all servers busy does not enter but goes elsewhere. Suppose that an arriving customer who finds at least one idle server is served by a randomly chosen one of that group; that is, an arrival finding k idle servers is...
Roblem Consider a single server queueing system where the customers arrive according to a Poisson...
roblem Consider a single server queueing system where the customers arrive according to a Poisson process with a mean rate of 18 per hour, and the service time follows an exponential distribution with a mean of 3 minutes. (1). What is the probability that there are more than 3 customers in the system? (2). Compute L, Lq and L, (3). Compute W, W and W (4). Suppose that the mean arrival rate is 21 instead of 18, what is the...
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 a two-server system in which a customer is served first by server 1, then by...
Consider a two-server system in which a customer is served first by server 1, then by server 2, and then leaves. The service time at server 1 is exponentially distributed with mean 15 minutes, the service time at server 2 is exponentially distributed with mean 10 minutes, and all service times are independent. When Alex arrives, he finds that Bob is currently with server 1, and Carl is currently with server 2. Find Alex's expected total time in the system...
I specifically need help with part c and d Problem #1 (10 points) Customers arrive to...
I specifically need help with part c and d
Problem #1 (10 points) Customers arrive to a fast food restaurant with two servers with interarrival times that follow an exponential distribution with a mean of 5 minutes. Service times (per server) also follow an exponential distribution with a mean of 8 minutes. There is enough space in the restaurant to accommodate a very large number of customers waiting to be served. (a) (3 points) What is the probability that at...
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.
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...
Problem 3 Consider a single-server queueing system that can hold a maximum of two customers excluding those being served. The server serves customers only in batches of two, and the service time (for a batch) has an exponential distribution with a mean of 1 unit of time. Thus if the server is idle and there is only one customer in the system, then the server must wait for another arrival before beginning service. The customers arrive according to a Poisson...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
2. [3] Suppose you arrive to a service system with three...
2. (3) Suppose you arrive to a service system with three parallel servers. All servers are basy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates μ1,P2, and μ3, what is the expected time you will spend in the system?
2. (3) Suppose you arrive to a service system with three parallel...
roblem Consider a single server queueing system where the customers arrive according to a Poisson process with a mean rate of 18 per hour, and the service time follows an exponential distribution with a mean of 3 minutes. (1). What is the probability that there are more than 3 customers in the system? (2). Compute L, Lq and L, (3). Compute W, W and W (4). Suppose that the mean arrival rate is 21 instead of 18, what is 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 a two-server system in which a customer is served first by server 1, then by server 2, and then leaves. The service time at server 1 is exponentially distributed with mean 15 minutes, the service time at server 2 is exponentially distributed with mean 10 minutes, and all service times are independent. When Alex arrives, he finds that Bob is currently with server 1, and Carl is currently with server 2. Find Alex's expected total time in the system...
I specifically need help with part c and d
Problem #1 (10 points) Customers arrive to a fast food restaurant with two servers with interarrival times that follow an exponential distribution with a mean of 5 minutes. Service times (per server) also follow an exponential distribution with a mean of 8 minutes. There is enough space in the restaurant to accommodate a very large number of customers waiting to be served. (a) (3 points) What is the probability that at...
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...
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