Probability characteristics cvaluation in queueing system with random requirements

We suggest a recursive algorithm for calculating the stationary probabilities and probability characteristics of queueing system with random resource requirements. Consider the system with multiple classes of resource requirements described by a random vector. Each class of customers requires a random vector of resources to be served. Unlike to well-known models with constant requirements of resource units we analyse model with random requirements with both discrete and continuous resources. The key difference from already analysed model with random requirements concerns the volume of released resources at the end of customer service. General model requires to store all vectors of occupied resources, while described model deals with the total volume of occupied resources. Upon departure from the system, customer releases not the same volume of resources as it occupied, but some random volume which is independent from previous system's state and incoming flow. It was proved that in case of Poisson arrivals and exponential service time the general system is equivalent to the simplified system that deals with only total amount of occupied resources. Proposed simplification lowers the complexity of calculation algorithms. Then, we consider aggregation of customers with the same class of requirements. Summing up stationary probabilities over each class, we derived a formula for the normalized average requirement. The computing performance significantly depends on length of vector of resources and number of customers. To avoid calculating of all k-fold convolutions for each set of vectors we suggest the recursive algorithm. The algorithm is applied for calculation of blocking probability and vector of average occupied resources. Queueing system with random resource requirements adequately models radio resource allocation in modern heterogeneous networks and forthcoming 5G networks. © Copyright 2017 for the individual papers by the papers' authors.