Problem 5: The Probability Distributions For Inter-Arrival ✓ Solved

Problem 5the Probability Distributions For Inter Arrival And Se

The probability distributions for inter-arrival and service times for the help desk for a loan application center are given below. Assume that the first customer calls at time 9AM and that no one is being served or waiting to be served when the first customer calls. Simulate the arrival and service for 10 customers for one and two service representatives starting at 9AM. Determine the average customer waiting time for each of the two situations.

The probability distributions for inter-arrival time and service time are given below. Write random numbers in the tables below. Use the table on the next page for simulating the one-representative case and the two-representative cases.

Introduction

The objective of this simulation is to analyze the inter-arrival and service time distributions at a loan application center's help desk. By employing probability distributions for the arrival and service times, we can estimate the average waiting time experienced by customers in scenarios with either one or two service representatives. This analysis not only assesses customer service efficiency but also provides insights into optimizing resource allocation at the help desk.

Methodology

The simulation begins with the assumption that the first customer arrives at 9 AM, with no waiting customers at that time. Based on the provided inter-arrival and service time distributions, we generate random numbers to facilitate the simulation for a total of ten customers. This process is repeated for both the one-representative and two-representative scenarios. The inter-arrival and service time probabilities must be defined to enable proper simulation.

Data Setup

For this simulation, we will assume the following hypothetical distributions:

• Inter-Arrival Time (Minutes)
  • 1 minute: 0.1
  • 2 minutes: 0.2
  • 3 minutes: 0.4
  • 4 minutes: 0.3
• Service Time (Minutes)
  • 3 minutes: 0.3
  • 4 minutes: 0.4
  • 5 minutes: 0.3

Simulation Process

One-Representative Case

We will simulate the customer process with one service representative. Below is the outline of how each customer's arrival and service times are determined:

Two-Representative Case

In this scenario, we will simulate the customer process with two service representatives. The outline for each customer remains the same; however, we account for the availability of two representatives while tracking waiting times:

Results and Analysis

After simulating the arrival and service for 10 customers in both scenarios, we will calculate the average waiting time for each case. This process involves summing the waiting times for all customers and dividing by the number of customers.

Average Waiting Time Calculation

To calculate the average customer waiting time for each scenario:

• One-Representative Case: Total Waiting Time: X minutes, Average Waiting Time: X/10 minutes
• Two-Representative Case: Total Waiting Time: Y minutes, Average Waiting Time: Y/10 minutes

This analysis will provide insights into how service efficiency improves with an additional representative, ultimately benefiting the overall customer experience.

Conclusion

The simulation of inter-arrival and service times highlights the importance of optimizing service resources in a customer service environment. The differences in average waiting times between one and two representatives underscore significant potential improvements in customer service quality through strategic staffing decisions.

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