Published Paper Details:

O'Brien (1954), Jackson (1954) and Hunt (1955) studied the problems of serial queues in the steady state with Poisson assumptions. In these studies, it is assumed that the unit must go through each service channel without leaving the system. Barrer (1955) obtained the steady - state solution of a single channel queuing model having Poisson input, exponential holding time, random selection where impatient customers leave the service facility after a wait of certain time. Finch (1959) studied simple queues with customers at random for service at a number of service stations in series where the arrival from outside was considered at the initial stage. Feedback is permitted either from the terminal server or from each server of the series to the queue waiting for service at that stage by imposing an upper limit on the number of customers in the system at any time. Singh(1984) studied the problem of serial queues introducing the concept of reneging. Singh and Umed (1994) worked on the network of queuing processes with impatient customers. Punam (2011) found the steady-state solution of serial queuing processes where feedback is not permitted. In our present work, the steady-state solutions are obtained for serial channels with feedback connected with non-serial queuing processes with reneging and balking and non-serial queuing processes with reneging and balking in which (i) M service channels in series are linked with N non-serial channels having reneging and balking. (ii) Feedback is permitted in M serial service channel from any channel to its pervious channel. (iii) A customer may join any channel from outside and leave the system at any stage after getting service. (iv) Poisson arrivals and exponential service times are followed. (v) The queue disciple is random selection for service. (vi) Waiting space is finite.