Question

Jobs arrive at a single-CPU computer facility with interarrival times the are IID exponential random variables with mean 1 minute. Each job specifies upon arrival the maximum amount of processing time it requires, and the maximum times for successive jobs are IDD exponential random variable with mean 1.1 minutes. However, if m is the specified maximum processing time for a particular job, the actual processing time is distributed uniformly between 0.55m and 1.05m. The CPU will never process a job for a more than its specified maximum; a job whose required processing time exceeds it s specified maximum leaves the facility without completing service. Simulate the computer facility until 1000 jobs have left the CPU if (a) jobs in the queue are processed in a FIFO manner, and (b) jobs in the queue are ranked in increasing order of their specified maximum processing time. For each case, compute the average and maximum delay in queue of jobs, the proportion of jobs that are delay in queues more than 5 minutes, and the maximum number of jobs ever in the queue. User stream 1 for the interarrival times, stream 2 for the maximum processing times, and stream 3 for the actual processing times. which operating policy would you recommend?

Answer 1

ꟷ> The input process is usually called the arrival process. Arrivals are called customers. In all models that we will discuss, we assume that no more than one arrival can occur at a given instant. For a case like a restaurant, this is a very unrealistic assumption. If more than one arrival can occur at a given instant, we say that bulk arrivals are allowed. Usually, we assume that the arrival process is unaffected by the number of customers present in the system. In the context of a bank, this would imply that whether there are 500 or 5 people at the bank, the process governing arrivals remains unchanged. There are two common situations in which the arrival process may depend on the number of customers present.

ꟷ> The first occurs when arrivals are drawn from a small population. Suppose that there are only four ships in a naval shipyard. If all four ships are being repaired, then no ship can break down in the near future. On the other hand, if all four ships are at sea, a breakdown has a relatively high probability of occurring in the near future. Models in which arrivals are drawn from a small population are called finite source models. Another situation in which the arrival process depends on the number of customers present occurs when the rate at which customers arrive at the facility decreases when the facility becomes too crowded. For example, if you see that the bank parking lot is full, you might pass by and come another day. If a customer arrives but fails to enter the system, we say that the customer has balked.

ꟷ> The phenomenon of balking was described by Yogi Berra when he said, “Nobody goes to that restaurant anymore; it’s too crowded.” If the arrival process is unaffected by the number of customers present, we usually describe it by specifying a probability distribution that governs the time between successive arrivals. The queue discipline describes the method used to determine the order in which customers are served. The most common queue discipline is the FCFS discipline (first come, first served), in which customers are served in the order of their arrival. Under the LCFS discipline (last come, first served), the most recent arrivals are the first to enter service. If we consider exiting from an elevator to be service, then a crowded elevator illustrates an LCFS discipline.

ꟷ> Sometimes the order in which customers arrive has no effect on the der in which they are served. This would be the case if the next customer to enter service is randomly chosen from those customers waiting for service. Such a situation is referred to as the SIRO discipline (service in random order). When callers to an airline are put on hold, the luck of the draw often determines the next caller serviced by an operator. Finally, we consider priority queuing disciplines. A priority discipline classifies each arrival into one of several categories. Each category is then given a priority level, and within each priority level, customers enter service on an FCFS basis. Priority disciplines are often used in emergency rooms to determine the order in which customers receive treatment, and in copying and computer time-sharing facilities, where priority is usually given to jobs with shorter processing times.