Question

The California border inspection station discussed in the prior question, is considering the addition of a...

The California border inspection station discussed in the prior question, is considering the addition of a second inspector. The vehicles would wait in one lane and then be directed to the first available inspector. Arrival rates would remain the same (36 per hour) and the new inspector would process vehicles at the same rate as the first (40 per hour). a. What would be the average length of the waiting line? b. What would be the average time that a vehicle must wait to get through the system? c. What proportion of the time would the inspection station be empty? d. What is the average utilization of each inspector?

Business   Operations-Management   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

This is a M/M/s queueing model, with number of servers, s = 2

Calculation of queue operating characteristics is following

a) Average length of waiting line (Lq) = 0.2285 (refer cell G13)

b) Average time in the system (W) = 0.0313 hours   (refer cell J13)

c) Proportion of time the insepction station would be empty (P0) = 0.3793   (refer cell E13)

d) Average utilization of each inspector (Rho)= 0.45   (refer cell F13)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
At a border inspection station, vehicles arrive at the rate of 8 per hour in a...
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average total time it takes for a vehicle to get...
Vehicles leaving North Portal, Saskatchewan arrive at US customs in Portal, North Dakota in accordance with...
Vehicles leaving North Portal, Saskatchewan arrive at US customs in Portal, North Dakota in accordance with a Poisson process. On average, 3 vehicles per hour arrive at the border crossing. There to greet them is Bullwinkle the Moose on behalf of the United States of America. Inspector Bullwinkle processes vehicles with exponential service times averaging 15 minutes. For some reason, people don't mind waiting in queue, or being inspected by a moose. However, once Bullwinkle starts an inspection, passengers get...
A mechanic at the Highway Department Garage repairs vehicles that break down at an average   of ?...
A mechanic at the Highway Department Garage repairs vehicles that break down at an average   of ? = 3 vehicles per hour. The mechanic can service a vehicle on an average of 15 minutes.  (20 Points) a. What is the utilization rate for this service system? b. What is the average time before the facility can return a breakdown to service? c. How much of that time is spent waiting for service? d. How many vehicles are likely to be waiting for...
A car wash has 10 available bays; however, the owners find that it is expensive to...
A car wash has 10 available bays; however, the owners find that it is expensive to have too many bays open when utilization is low because there are costs associated with having a bay open, such as electricity for lighting and costs for cleaning. Thus, they would like to have only as many bays open as needed to ensure average customer wait time (in line) of no more than five minutes. (Corporate strategy emphasizes low cost over short wait time)....
All trucks traveling on Freeway 99 between Sacramento and Fresno are required to stop at a...
All trucks traveling on Freeway 99 between Sacramento and Fresno are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 165 per 8-hour day, and the station can weigh, on the average, 180 trucks per 8-hour day. Determine the average time spent waiting and being weighed at the weigh station by each truck. Determine the average waiting time before being weighed for each truck. Determine the average number of trucks waiting Determine...
Eat & Gas convenience store operates a two-pump gas station. The lane leading to the pumps...
Eat & Gas convenience store operates a two-pump gas station. The lane leading to the pumps can house at most 3 cars, excluding those being served. Arriving cars go elsewhere if the lane is full. The distribution of arriving cars is Poisson with mean 20 per hour. The time to fill up and pay for the purchase is exponential with mean 6 minutes. What is the percentage of cars that will seek business elsewhere? What is the percentage of time...
A gas station with two pumps does not allow drivers to pump their gas and has...
A gas station with two pumps does not allow drivers to pump their gas and has a service attendant for each pump. Potential customers (i.e. cars) arrive according to KinKo, a process at a rate of 40 cars per hour. If the two pumps are busy, then arriving cars wait in a single queue to be served in the order of arrival by the first available pump. However, cars cannot enter the station to wait if there are already two...
Trucks are required to pass through a weighing station so that they can be checked for...
Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 35 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour. a. How many trucks would you expect to see at the weighing station, including those being inspected? b.If a truck was just arriving at the station,...
Trucks are required to pass through a weighing station so that they can be checked for...
Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 18 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can inspect 15 trucks an hour. a. How many trucks would you expect to see at the weighing station, including those being inspected? Ls=_____trucks b.If a truck was just arriving at the...
1.1 (M/M/1) model - use the qtsPlus or other software to answer the questions. In a...
1.1 (M/M/1) model - use the qtsPlus or other software to answer the questions. In a grocery store, there is one cashier. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 18 customers per an hour. Customers are served in order of arrival (FCFS: first come first service). The service time (i.e. the time needed for scanning the items and processing payment) is exponentially distributed. The mean service time is 3 minutes. A) Once...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT