In this problem, you are requested to develop a spreadsheet discrete event simulation for a simple queuing system. The queuing system consists of a single LIFO (last in, first out) queue having infinite capacity followed by a single server having one resource.

Samples from an arrival process A are used to generate random variates for entity inter-arrival times. Similarly, samples from a service time process S are used to generate service times for the server. The samples from A and S are listed in the following sets. You are to assume that each sample value is generated when needed in the simulation; the entire random variate streams are not visible to the simulation during execution.

A = { 1, 1, 1, 2, 1, 3, 2, 1, 2, 1, 4, }

S = { 3, 1, 2, 1, 1, 2, 3, 1, 1, 4, 2, }

The simulation starts empty and idle at t = 0. The simulation terminates when simulation time reaches t = 10. When two or more events occur at the same time, events are processed in the following order: depart events; terminate events; and arrive events. Simultaneous events of the same type are processed in increasing order of the entities affected.

Answer the following questions concerning this simulation.

A. Identify a minimal set of state variables required for this system. Identify the values that each state variable can assume. Also identify the minimal set of event types for this system.

B. Construct an Event History Table for this simulation. This table contains four columns arranged in the order listed: (1) Event Name; (2) Event Type; (3) Event Time; and (4) Entity Affected. The rows of this table correspond to simulation events arranged in order of occurrence. Events are named by assigning an integer that indicates the order of occurrence.

C. Construct an Entity History Table for this simulation. This table contains four columns arranged in the order listed: (1) Entity Name; (2) Arrival Time at Queue; (3) Arrival Time at Server; and (4) Departure Time from Server. The rows of this table correspond to entity names arranged in order of arrival at the system. Entities are named by assigning an integer that indicates the order of arrival.

D. Accurately sketch the system state variables as a function of time. Use a separate plot for each state variable, but use a common time scale for each plot.

E. Determine the following performance measures for this system: (1) Average delay in queue; (2) Average number in queue; (3) Maximum number in queue; (4) Average flow time; (5) Maximum flow time; and (6) Server utilization.