Queueing analysis is a mathematical technique for analyzing waiting lines. In a simple waiting line, a customer arrives, joins a queue, is serviced, and leaves. Queueing theory assumes exponential arrival and service rates. Generally, this exponential distribution is Poisson. Thus, for a queueing system with low traffic intensity, the expected number of customers in the queue is small. However, with a bursty input process, long queues may build up in a short time. We studied various length traffic queueing systems, some with bursty input processes. We examined the distributions of queue lengths, waiting times, busy and active periods, and their corresponding expansions. If time permitted, we would give special attention to some conditional distributions of queue lengths, waiting times, and system-active periods. The expansions would provide a potential asymptotic approach to the computation of various descriptors of queueing systems. The coefficients of those expansions would reflect some important features of episodic queues and prioritization methods, which were not included, in depth, in this project. We also studied graphical representations of the numerical results of approximations and of the effect of the burstiness of the input and service processes on the queues. As a result, the program generated a practical output of potential scheduling matrices.