The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the average time a cab must wait for a fare?

The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the average time a cab must wait for a fare?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 21P

See similar textbooks

Similar questions

Customers arrive at the lobby of the exclusive and expensive Ritz Hotel at the rate of 40 per hour (Poisson distributed) to check in. The hotel normally has three clerksavailable at the desk to check guests in. The average timefor a clerk to check in a guest is four minutes (exponentially distributed). Clerks at the Regency are paid $12 perhour and the hotel assigns a goodwill cost of $2 per minutefor the time a guest must wait in line. Determine if the present check-in system is cost effective; if it is not, recommend what hotel management should do
Partially completed products arrive at a workstation in amanufacturing operation at a mean rate of 40 per hour(Poisson distributed). The processing time at the workstation averages 1.2 minutes per unit (exponentially distributed). The manufacturing company estimates that each unitof in-process inventory at the workstation costs $31 perday (on the average). However, the company can add extraemployees and reduce the processing time to 0.90 minuteper unit at a cost of $52 per day. Determine whether thecompany should continue the present operation or addextra employees.
You are in charge of a quarry that supplies sand and stone aggregates to your company’s construction sites. Empty trucks from construction sites arrive at the quarry’s huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. Atthe station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, nine empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 6 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and to add a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. Thearrival rate of trucks would change to six per hour, and…
The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air trafficcontroller to land planes. It takes an airplane 12 minutes to land and clear the runway. Planes arriveat the airport at the rate of four per hour. The FAA has a rule that an air traffic controller can, on average, land planes a maximum of 45 minutes out of every hour. There must be 15 minutes of idle time available to relieve the tension. Will this airport have to hire an extra air traffic controller?
During the evening hours, an average of 52 customers can be found in Sachi’s Sports Bar. About 40 customers arrive each hour. Using Little’s Law, how long does each customer stay at Sachi’s?