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Some persons are arriving at a Caribbean rail ticket office during the morning peak commuter period frequently have to wait for service. There is one clerk who issues tickets and provides an information service for passengers. The Boss has received complaints regarding the time passengers spend in the queue waiting to be served, and she wishes to investigate possible methods of reducing the queueing time. Possible ideas include employing a second ticket clerk who could either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be to collect fares on the train. The manager decided to collect data on arrivals and service times over a number of days, and her figures are summarized T Inter - arrival time (Secs) 0 to under 30 30 to under 60 60 to under 90 90 to under 120 Frequency (%) 55 30 10 5

Some persons are arriving at a Caribbean rail ticket office during the morning peak commuter period frequently have to wait for service. There is one clerk who issues tickets and provides an information service for passengers. The Boss has received complaints regarding the time passengers spend in the queue waiting to be served, and she wishes to investigate possible methods of reducing the queueing time. Possible ideas include employing a second ticket clerk who could either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be to collect fares on the train. The manager decided to collect data on arrivals and service times over a number of days, and her figures are summarized T Inter - arrival time (Secs) 0 to under 30 30 to under 60 60 to under 90 90 to under 120 Frequency (%) 55 30 10 5

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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1. Compute the midpoints for arrival and service times and apply it to construct the 
appropriate random number mappings for the random variables starting from 00

2. Simulate 15 customers arriving at the using the random numbers given below

3. What is the average time a customer is in the system (wait plus service time)

THIS IS NOT A GRADED ASSIGNMENT THIS IS PRACTICE FOR EXAMS

Hint (midpoint for 60 to under 90 (60+90)/2=75 sec) Customer Interarrival time Service Time 11 12 13 14 15 1 2 3 0.08 0.87 0.15 Random Numbers To Be Used in the Simulation 4 5 6 7 8 9 10 0.04 0.52 0.46 0.96 0.1 0.02 0.76 0.72 0.46 0.96 .00 0.27 0.73 0.76 0.25 0.11 0.47 0.28 0.83 0.52 0.39 0.68 0.32 0.1 0.62 0.25 0.9 Use the following headings to complete the simulation Time Between Customer RN Arrivals Arrival Wait for Begin Time Service service Time in Service System RN Service End Time
Transcribed Image Text:Hint (midpoint for 60 to under 90 (60+90)/2=75 sec) Customer Interarrival time Service Time 11 12 13 14 15 1 2 3 0.08 0.87 0.15 Random Numbers To Be Used in the Simulation 4 5 6 7 8 9 10 0.04 0.52 0.46 0.96 0.1 0.02 0.76 0.72 0.46 0.96 .00 0.27 0.73 0.76 0.25 0.11 0.47 0.28 0.83 0.52 0.39 0.68 0.32 0.1 0.62 0.25 0.9 Use the following headings to complete the simulation Time Between Customer RN Arrivals Arrival Wait for Begin Time Service service Time in Service System RN Service End Time
Some persons are arriving at a Caribbean rail ticket office during the morning peak commuter period frequently have to wait for service. There is one clerk who issues tickets and provides an information service for passengers. The Boss has received complaints regarding the time passengers spend in the queue waiting to be served, and she wishes to investigate possible methods of reducing the queueing time. Possible ideas include employing a second ticket clerk who could either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be to collect fares on the train. The manager decided to collect data on arrivals and service times over a number of days, and her figures are summarized | Inter - arrival time (Secs) 0 to under 30 30 to under 60 60 to under 90 90 to under 120 Service time (secs) 20 to under 30 30 to under 40 40 to under 50 50 to under 60 60 to under 90 Frequency (%) 55 30 10 5 Frequency (%) 17 28 25 20 10
Transcribed Image Text:Some persons are arriving at a Caribbean rail ticket office during the morning peak commuter period frequently have to wait for service. There is one clerk who issues tickets and provides an information service for passengers. The Boss has received complaints regarding the time passengers spend in the queue waiting to be served, and she wishes to investigate possible methods of reducing the queueing time. Possible ideas include employing a second ticket clerk who could either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be to collect fares on the train. The manager decided to collect data on arrivals and service times over a number of days, and her figures are summarized | Inter - arrival time (Secs) 0 to under 30 30 to under 60 60 to under 90 90 to under 120 Service time (secs) 20 to under 30 30 to under 40 40 to under 50 50 to under 60 60 to under 90 Frequency (%) 55 30 10 5 Frequency (%) 17 28 25 20 10
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