A taxi company has three cabs. Calls come in to the dispatcher at times of a...
A taxi company has three cabs. Calls come in to the dispatcher at times of a Poisson process with rate 2 per hour. Suppose that each requires an exponential amount of time with mean 20 minutes, and that callers will hang up if they hear there are no cabs available. Find the transition rate matrix for the number of available cabs. (Use a continuous time Markov chain)
Homework Answers
Add Answer to:
A taxi company has three cabs. Calls come in to the dispatcher
at times of a...
City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The...
City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to City Cab use a common telephone number. When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed. Callers who receive a busy signal can call back later or call another cab company for service. Assume that the arrival of calls follows a Poisson distribution, with a mean of 40 calls per hour,...
City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The...
City Cab, Inc., uses two dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to City Cab use a common telephone number. When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed. Callers who receive a busy signal can call back later or call another cab company for service. Assume that the arrival of calls follows a Poisson distribution, with a mean of 40 calls per hour,...
Consider the call center model with 8 agents and ability to put at most 4 callers...
Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. exponential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of the agents is...
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on ho...
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. expo- nential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of...
Problem 1. Consider a telephone system with three lines. Calls arrive according to a Poisson process...
Problem 1. Consider a telephone system with three lines. Calls arrive according to a Poisson process at a mean rate of 6 per hour. The duration of each call has an exponential distribution with a mean of 20 minutes. If all lines are busy, calls will be put on hold until a line becomes available. (a Determine the steady-state probability that a call will be answered immediately (not put on hold) (b) Determine the steady-state probability distribution of the number...
C) Janson's is considering adding a second clerk to take calls. the store's cost would be...
C) Janson's is considering
adding a second clerk to take calls. the store's cost would be the
same $12 per hour. The total cost ( service cost + waiting cost) =
$___per hour (round your response to two
decimal places)
By hiring the second clerk, the total cost savings per hour for
Janson's = $___ per hour (round your response to two
decimal places)
Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk...
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In...
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on "hold" until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold lines) are busy, a potential customer gets a busy signal, and it is assumed she calls another ticket office, so that her business is lost. The calls and attempted calls occur randomly i.e., according...
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...
People's Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by...
People's Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 8 minutes. Calls are arriving according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per...
Suppose the number of phone calls arriving at an answering service follows a Poisson process with...
Suppose the number of phone calls arriving at an answering service follows a Poisson process with the rate lambda = 60 (or equivalently, the interarrival times are iid exponential random variables with mean 1 minute). a.) Let T(I,j) denote the time interval from the ith arrival the jth arrival. The correlation between T(10,50) and T(20,60) is equal to ____________. b.) The correlation between T(0,20) and T(0,60) is equal to ________________.
Problem 5 Consider the call center model with 8 agents and ability to put at most 4 callers on hold. Calls arrive according to a Poisson process with rate 60 calls per hour. Call handling times are i.i.d. expo- nential random variables with mean 6 minutes. Any call that arrives when all agents are busy and 4 callers are on hold, is lost. What is the expected time when all agents are busy in an 8-hour shift? Assume none of...
Problem 1. Consider a telephone system with three lines. Calls arrive according to a Poisson process at a mean rate of 6 per hour. The duration of each call has an exponential distribution with a mean of 20 minutes. If all lines are busy, calls will be put on hold until a line becomes available. (a Determine the steady-state probability that a call will be answered immediately (not put on hold) (b) Determine the steady-state probability distribution of the number...
C) Janson's is considering
adding a second clerk to take calls. the store's cost would be the
same $12 per hour. The total cost ( service cost + waiting cost) =
$___per hour (round your response to two
decimal places)
By hiring the second clerk, the total cost savings per hour for
Janson's = $___ per hour (round your response to two
decimal places)
Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk...
An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on "hold" until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold lines) are busy, a potential customer gets a busy signal, and it is assumed she calls another ticket office, so that her business is lost. The calls and attempted calls occur randomly i.e., according...
People's Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 8 minutes. Calls are arriving according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per...
Most questions answered within 3 hours.
-
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 39 minutes ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 1 hour ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 1 hour ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 1 hour ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 2 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 2 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 3 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 3 hours ago -
Michaella, age 23, is a full-time law student and is claimed by
her parents as a...
asked 3 hours ago -
Why are polymers not typically casted into products?
asked 3 hours ago -
When rolling a die 129 times, what is the probability of rolling
a 6 no more...
asked 3 hours ago -
4. A call option currently sells for $7.75. It has a strike
price of $85 and...
asked 3 hours ago