1. **Problem Statement:** Prepare a simulation table showing system states, future event lists, and cumulative statistics until the clock reaches time 15, using the given interarrival and service times. The stopping event is at time 30. 2. **Given Data:** - Interarrival times: $1, 5, 6, 3, 8$ - Service times: $3, 5, 4, 1, 5$ 3. **Key Concepts:** - **Interarrival time** is the time between arrivals of customers. - **Service time** is the time taken to serve a customer. - The **clock** advances to the next event time. - **Future Event List (FEL)** keeps track of upcoming arrivals and departures. - **Cumulative statistics** include total customers served, waiting time, etc. 4. **Step-by-step Simulation:** **Step 1: Initialize** - Clock = 0 - Schedule first arrival at $0 + 1 = 1$ - Server is idle - FEL = {Arrival at 1} **Step 2: Process events until clock reaches 15** | Event | Clock | Event Type | System State | FEL (next events) | Notes | |-------|-------|------------|--------------|-------------------|-------| | 1 | 1 | Arrival 1 | Customer 1 arrives, server idle, starts service | Departure at $1+3=4$, Arrival 2 at $1+5=6$ | Server busy | | 2 | 4 | Departure 1 | Customer 1 departs, server idle | Arrival 2 at 6 | Server idle | | 3 | 6 | Arrival 2 | Customer 2 arrives, server idle, starts service | Departure at $6+5=11$, Arrival 3 at $6+6=12$ | Server busy | | 4 | 11 | Departure 2 | Customer 2 departs, server idle | Arrival 3 at 12 | Server idle | | 5 | 12 | Arrival 3 | Customer 3 arrives, server idle, starts service | Departure at $12+4=16$, Arrival 4 at $12+3=15$ | Server busy | | 6 | 15 | Arrival 4 | Customer 4 arrives, server busy, waits in queue | Departure at 16, Arrival 5 at $15+8=23$ | One in queue | **Step 3: Summary at clock 15** - Customers arrived: 4 - Customers served: 2 - Customers in service: 1 - Customers waiting: 1 - Next events: Departure at 16, Arrival at 23 5. **Explanation:** - Each arrival schedules the next arrival. - If server is busy, arriving customers wait. - Departures free the server and start service for waiting customers. - Simulation stops at clock 15 for this part. 6. **Final Answer:** Simulation table and states as above until time 15. --- **Note:** The second problem (Able-Baker call center simulation) is not solved here as per instructions to solve only the first problem.