## 1 Introduction  
Asynchronous Transfer Mode (ATM) networks are connection-oriented networks for cell relay that support some services such as video, voice streaming, and data communications. At a multiplexer in an ATM network, the admissible cell loss probability needs to be less than \(10^{-12}\) for real-time services such as voice and video. Evaluating this extremely small probability by simulation is a challenging task. Monte Carlo (MC) is an effective technique for performing simulations of problems that cannot be solved theoretically. However, the disadvantage of the Monte Carlo method is that it consumes a large amount of simulation time. The Importance Sampling technique is useful for simulations in the fields of communication and engineering [1; 2]. As an improvement of the Monte Carlo method, IS simulation generated the target events more frequently by using another distribution density function. It is crucial to ascertain the most advantageous settings for the distribution in the simulation. The distribution that produces the estimate with the lowest variance is called the optimal simulation distribution. The determination of optimal distribution in IS simulation has been studied in many papers, including heuristic and theoretical methods. In [3], the authors proposed a heuristic method to search parameters for optimal simulation distribution. Another method was proposed in [1], using an annealing algorithm to obtain optimal simulation distribution. These methods search the large domain of parameters, so they require computation time. The author in [4] introduced a theoretical approach that utilizes big deviation theory to determine the most efficient simulation distribution for the tail probability in the MMPP/D/1 queue system. Then [5] solved the general case of \(n\) states of the MMPP/D/1 queue. These theoretical methods have less computing time compared with the heuristic methods. The MMPP, also known as the Markov-Modulated Poisson Process, is a stochastic process that combines both a Poisson process and a Markov chain. In this process, the intensity of the Poisson process is determined by the current state of the Markov chain. The MMPP is capable of modeling the sudden increase in video, voice, and data traffic on the Internet. Let us examine the two-state Markov-Modulated Poisson Process (MMPP). The symbol \(\lambda_{i}\) represents the mean arrival rate of the Poisson process in state \(i\), where \(i\) can take on the values of either 0 or 1. Additionally, \(r_{ij}\) represents the probability of transitioning from state \(i\) to state \(j\), where both \(i\) and \(j\) can be either 0 or 1. Figure 1 depicts the representation of a two-state Markov-Modulated Poisson Process (MMPP). The MMPP/D/1 queue model is characterized by an arrival process following the MMPP model, deterministic service times, and an unlimited buffer capacity. Let \(\mu\) be the service rate of the MMPP/D/1 queue. Therefore, \(1/\mu\) represents both the duration of serving a single packet and the size of a time slot. The MMPP/D/1 queue is a suitable model for simulating the arrival of packets in an ATM network multiplexer. Due to the minuscule likelihood of packet loss in an ATM network, determining it using the traditional Monte Carlo method is a time-consuming process. We employed the IS (Importance Sampling) technique to compute the probability of packet loss in the MMPP/D/1 queue through an ATM network simulation. By decreasing the processing speed at the queue, we may carry out estimations in real time. [PERSON] [6] proposed a method to estimate the Tail Probability of FIFO queue length by using Importance Sampling. A virtual queue, ISQL counter, was implemented to decrease the service rate. Consequently, the queue length increases quickly and tail events happen more frequently. In this way, the estimation of the Tail Probability can be calculated faster and more exactly.