In the paper a finite-capacity discrete-time queueing system with geometric interarrival times and generally distributed processing is studied. Every time when service station becomes idle it goes for vacation of random duration that can be treated as power-saving mechanism. Application single policy one way to achieve symmetry in terms operating costs. A differential equations transient condit...

A GI/M/1-type queueing system with finite buffer capacity and AQM-type packet dropping is investigated. Even when the buffer is not saturated an incoming packet can be dropped (lost) with probability dependent on the instanteneous queue size. The system of integral equations for time-dependent queue-size distribution conditioned by the number of packets present in the system initially is built ...

Join the Shortest Queue (JSQ) is a popular routing policy for server farms. However, until now all analysis of JSQ has been limited to First-Come-First-Serve (FCFS) server farms, whereas it is known that web server farms are better modeled as Processor Sharing (PS) server farms. We provide the first approximate analysis of JSQ in the PS server farm model for general job size distributions, obta...

A multiple optional vacation policy for the unreliable server batch arrival queueing system with essential and multi optional services under N-policy is investigated. According to vacation policy, the server takes an essential phase of vacation after the completion of service of an individual customer when queue becomes empty. On returning from the vacation, if the server finds the queue empty,...

 In this paper, a bulk queueing system with multiple vacations under a restricted admissibility policy of arriving batches is considered. Arrivals occur in bulk according to Poisson process. But all the arrivals are not considered for service. During the busy period of the server, the arrivals are admitted with probability ‘ ’, whereas, with probability ‘  ’, they are admitted when the serve...

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system’s stationa...

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoul...

We consider the following stochastic bin packing process: the items arrive continuously over time to a server and are packed into bins of unit size according to an online algorithm. The unpacked items form a queue. The items have random sizes with symmetric distribution. Our first contribution identifies some monotonicity properties of the queueing system that allow to derive bounds on the queu...

We present an approximate analysis of a discrete–time queue with correlated arrival processes of the so–called M |G|∞ type. The proposed heuristic approximations are developed around asymptotic results in the heavy and light traffic regimes. Investigation of the system behavior in light traffic quantifies the differences between the gradual M |G|∞ inputs and the point arrivals of a classical GI...