In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machi...

Various transportation services exist, such as ride-sharing or shared taxis, in which customers receive a batch of flexible sizes and share fees. In this study, we conducted an equilibrium analysis variable service model who observe no waiting incomplete can strategically select size to maximize the individual utilities. We formulated three-dimensional Markov chain created book-type transition ...

We study a vacation queueing model where an arriving customer, upon finding the server to be on vacation, is offered opportunity pay fee instantaneously end server's which referred as pay-to-activate-service (PTAS). If no one utilizes PTAS, service will automatically resume when system's workload reaches critical level. investigate customers' equilibrium strategies: (i) joining or balking and (...

We consider the single server Markovian queue and we assume that arriving customers decide whether to enter the system or balk based on a natural rewardcost structure, which incorporates their desire for service as well as their unwillingness to wait. We suppose that the waiting space of the system is partitioned in compartments of fixed capacity for a customers. Before making his decision, a c...

We consider customer joining behaviour for a system that consists of a FCFS queue with Bernoulli feedback. A consequence of the feedback characteristic is that the sojourn time of a customer already in the system depends on the joining decisions taken by future arrivals to the system. By establishing stochastic order results for coupled versions of the system, we prove the existence, and unique...