A : Elements of Queueing Theory

APPENDIX A: ELEMENTS OF QUEUEING THEORY In a packet radio network, packets/messages are forwarded from node to node through the network by entering a buffer (queue) of a certain length in each node and waiting for their turn to be transmitted to the next node. Also, call access to a network with a given capacity is modeled as a process with certain distribution of call arrival times and certain distribution of call service times. A number of different classes of queueing models are used in this field to analyze queueing delays or server (or network access) blocking probabilities. In order to generalize the presentation the elements in the queue (packets, messages, calls, etc.) will be referred to as customers. The problems nowadays become even more challenging in wireless cellular networks with handoffs, multimedia traffic and differentiated QoS. The key element in this analysis is a proper model for these distributions. The very first results in this field are based on the most common stochastic queueing models which assume that message (call) interarrival and service times obey the exponential distribution or, equivalently, that the arrival rate and service rate follow a Poisson distribution. In other words, if the arrival rate is λ , the probability of having n arrivals in an interval t is given as