Application of queueing models for banking transactions / Boshra Abdela{u221E}ziz Shehata Khattab ; Supervised Elham Shoukry Mohamed , Salwa Mahmoud Assar

Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

Queueing theory is a mathematical approach applied to analyze the waiting lines or queues. It uses models to represent the various types of queueing systems. This thesis aimed to apply some queueing models which are suitable for banking transactions in order to obtain expressions of some performance measures. The study has used the Markovian models (Poisson for arrivals, exponential for service times) for two servers and one queue with first-come first served queue discipline (M/M/2: FCFS/ {u221E} / {u221E} ) as an example of queueing models with multiple servers to determine the optimal number of servers and the optimal service rate by operating costs. The probability generating function has been used to estimate the steady-state probabilities for the Markovian models for two servers and two queues with two classes of priority as a queue discipline (M/M/2: PRI/ {u221E} / {u221E} ) and Markovian models with multiple queues and multiple classes of priority for homogeneous and heterogeneous servers (M/M/S: PRI/ {u221E} / {u221E} ). A comparative study between each type of these models has been introduced. The matrix geometric method has also been used to derive the stationary distribution for the Markovian models with single server subject to breakdown ATM machine (M/M/1: FCFS/ {u221E} / {u221E} ) and finally, a comparative study between the two models with and without breakdown has also been introduced

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