ایمان مخدوم

In this article, a queuing system with finite capacity, referred to as M/M/m/K, is analyzed for m ≥ 2, where K represents the system's capacity and m indicates the number of servers. Initially, a function known as the system cost function is introduced. This function is based on the number of customers present in the queue and the number of servers available. The main objective is to identify the optimal number of servers, termed mOpt, that minimizes the system cost function. This optimal configuration, denoted as M/M/mOpt/K, is termed the optimal system. To illustrate the concept, a numerical example is provided, showcasing various values of K to determine the optimal systems. The analysis covers key performance metrics such as the average number of customers in the queue and the entire system, the average waiting time of the customers both in the queue and the system, and a metric referred to as the average degree of customer satisfaction within these queuing systems. Through this comprehensive approach, the study aims to provide valuable insights into optimizing queuing systems for better efficiency and customer satisfaction.

Additive noise channels are the most commonly used channels in signal processing. In these channels the received signal, random variable Y, is composed of a transmitted signal, random variable X, and an additive noise, random variable Z. One of the important problems studied on the received signal is the entropy of random variable Y. When additive noise Z is an independent Gaussian random variable with zero mean and unit variance, the elegant algebraic connection between differential entropy of output signal Y and Fisher information is stated through a relation known as the De Bruijn’s identity. In this paper, we first obtain a general relation for differentials of conditional distribution of output signal and use it to prove the relationship between the first derivative of differential entropy of output signal and its Fisher information. This method can be used for extending De Bruijn’s identity when the additive noise is distributed as another useful statistical distributions.