Queuing system 'Expections' their affects and non-queue state : a new stochastic approach - Bhagat Singh Azad, Harpreet Sigh (2014)
Most queuing models are based on organized behavior of customers served by a server or multiple servers. However, there are many instances that the queuing model does not stand by real world queue ethics. The consequences can go towards non-queue state caused by overcrowding and cultural background of the customers. This research portrays the successive outcomes that sourced non-queue state due to customer ignored behaviors as well as the unsystematic policy of a single serving system which becomes the main research problem. Such activities are termed as 'exceptions' and their disturbances in queuing system. The main objective of this research is to present 'exceptions', their affects and to resolve the non-queue state. It is important so that the waiting time distribution, behaviour of the system during 'exceptions' and queuing system can be evaluated, demonstrated and reinstated to a single server queuing state, respectively. A non-queue is a state addressed when system utilization goes beyond I 00 percent. Furthermore, this would indicate no formal queue at all as customers could be assumed at random locations. This research will explain the state of the system during 'exception' and non-queue transformation largely with the support of probability theory in time index values. Various 'exceptions' categories with constructed waiting time probability models and their results have proven that the customers large waiting do actually overcrowd the queuing system. This thesis discusses 'exceptions' affects through the Markov chain, random walk and birth-death process. The above concepts illustrate system behaviour, as 'exception' that disrupts services. In exceptional case, stochastic matrix considered two types such as actual job and 'exception' to occur during state transition. Their limitation is further simplified by random walk in convolution idea. The system parameters such as late departures, queue loss and others are affirmed in continuous-time by birth-death process. Simulation of change of discrete-event of queuing system such as service times shows, in long-run on averages service time fluctuates, utilization gets large, service finishing late and customers get increased in the system causing non-queue state. A platform of dissimilar manners used by stochastic process in non-queue transformation analysis. One of the manner employed are Markov conditional selection procedure is presented to recover queuing system through selecting and ordering random states. In other manner, random state(s) proceeds to get in order are expanded by proceeding walk and multinomial-pure death view. The interrelation of such models is grounded through the random states and distance decays by an interval. All such manners in stochastic process have likely to bring into being a queuing model after non-queue transformation. This research finds that the stochastic process has tremendous potential to model 'exception' outcomes and to restore the 'exception' eventual affects.