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b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan taburan Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai kebarangkalian bahawa tiada kereta dalam sistem. iii) Compute the average time that a car spends in the system. [Kirakan purata masa kereta yang diperuntukkan dalam sistem.

b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan taburan Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai kebarangkalian bahawa tiada kereta dalam sistem. iii) Compute the average time that a car spends in the system. [Kirakan purata masa kereta yang diperuntukkan dalam sistem.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan tahuran Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai kebarangkalian bahawa tiada kereta dalam sistem.] Compute the average time that a car spends in the system. [Kirakan purata masa kereta yang diperuntukkan dalam sistem.I i11)
Transcribed Image Text:(b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan tahuran Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai kebarangkalian bahawa tiada kereta dalam sistem.] Compute the average time that a car spends in the system. [Kirakan purata masa kereta yang diperuntukkan dalam sistem.I i11)
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