Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential...

Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential with means of 0.5 and 1 minutes, respectively. Stand has 3 spots that taxis can park while waiting for the arriving customers. Arriving taxis leaves the stand when all the spots are occupied. Similarly, arriving customers are also lost when there is no taxi in the stand.

a. Model this system as a birth and death process by defining the state and the state space, and drawing the rate diagram.
b. Compute the steady-state probabilities.
c. What is the expected number of taxis waiting at the stand in the long run?

Solutions

Expert Solution

ANSWER::

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential...

Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential with means of 0.5 and 1 minutes, respectively. Stand has 3 spots that taxis can park while waiting for the arriving customers. Arriving taxis leaves the stand when all the spots are occupied. Similarly, arriving customers are also lost when there is no taxi in the stand. a. Model this system as a birth and death process by defining the state and the state...

For the purpose of using the chi-square test for inter-arrival data fitting against exponential distribution (goodness-of-fit)...

For the purpose of using the chi-square test for inter-arrival data fitting against exponential distribution (goodness-of-fit) for which the class intervals are not given, the analyst must determine the class interval endpoints. Assume that based on the collected data, the average inter-arrival time is 14.62 minutes. Assume that number of class intervals to be used for data classification is equal to 5. Calculate the endpoint of the first interval, Le. at knowing that a0-0 and that the data are in...

Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...

Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates μ1 and μ2, with μ1 > μ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on λ,μ1,μ2 for this system to be stable, i.e., the queue does not grow indefinitely long. b) Under that condition, and the long-run proportion of time that server 2 is busy.

Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...

Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates µ1 and µ2, with µ1 > µ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on λ, µ1, µ2 for this system to be stable, i. e., the queue does not grow infinitely long. b) Under that condition, find the long-run proportion of time that server 2 is busy.

At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed....

At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed. Arriving (actually departing) passengers go through a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 3 passengers per minute, where the time to check a passenger is also exponentially distributed. Why is this an M/M/1,...

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting...

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation. Bank A (single line): 6.5 6.6 6.7 6.9 7.1 7.3 7.4 7.6 7.7 7.8 Bank B (individual lines): 4.4 5.4 5.7 6.2 6.7 7.7 7.8 8.4 9.4 9.9 The...

The data table contains waiting times of customers at a bank, where customers enter a single...

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 2.3 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.01. Complete parts (a) through (d) below. customer waiting times (in minutes) 8.1 7.2 6.4...

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting...

Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation. Bank A (single line): 6.6 nbsp 6.6 nbsp 6.7 nbsp 6.8 nbsp 7.0 nbsp 7.3 nbsp 7.5 nbsp 7.7 nbsp 7.7 nbsp 7.8 Bank B (individual lines): 4.4 nbsp...

The data table contains waiting times of customers at a bank, where customers enter a single...

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.8 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.05. 1. Compute the test statistic. 2.Find the P-value of the test statistic. 6.8 7.4...

Waiting times (in minutes) of customers in a bank where all customers enter a single waiting...

Waiting times (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two samples, then compare the two sets of results. Single Line 6.5 6.6 6.7 6.8 7.0 7.1 7.5 7.6 7.6 7.6 Individual Lines 4.2 5.4 5.8 6.2 6.5 7.6 7.6 8.6 9.2 9.9 The mean waiting time...

Subjects