A pseudoconservation law for a time-limited service polling system with structured batch poisson arrivals

AbstractWe consider a cyclic-service queueing system (polling system) with time-limited service, in which the length of a service period for each queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then proceeds to the next queue. The customer whose service is interrupted due to the timer expiration is attended according to the nonpreemptive service discipline. For the cyclic-service system with structured batch Poisson arrivals (Mx/G/1) and an exponential timer, we derive a pseudoconservation law and an exact mean waiting time formula for the symmetric system

Queueing models for appointment-driven systems.

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue(also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decisionmaking concerning server capacity (e.g. how often, when and for how long should a server be online). We develop an ew model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.Queueing system; Appointment system; Vacation model; Overtime; Waiting list;

Queueing system with vacations after a random amount of work

This paper considers an M/G/1 queue with the following vacation discipline. The server takes a vacation as soon as it has served a certain amount of work since the end of the previous vacation. If the system becomes empty before the server has completed this amount of work, then it stays idle until the next customer arrival and then becomes active again. Such a vacation discipline arises, for example, in the maintenance of production systems, where machines or equipment mainly degrade while being operational. We derive an explicit expression for the distribution of the time it takes until the prespecified amount of work has been served. For the case the total amount of work till vacation is exponentially distributed, we derive the transforms of the steady-state workload at various epochs, busy period, waiting time, sojourn time, and queue length distributions

An analytical model for input-buffered optical packet switches with reconfiguration overhead

The overhead associated with reconfiguring a switch fabric in optical packet switches is an important issue in relation to the packet transmission time and can adversely affect switch performance. The reconfiguration overhead increases the mean waiting time of packets and reduces throughput. The scheduling of packets must take into account the reconfiguration frequency. This work proposes an analytical model for input-buffered optical packet switches with the reconfiguration overhead and analytically finds the optimal reconfiguration frequency that minimizes the mean waiting time of packets. The analytical model is suitable for several round-robin (RR) scheduling schemes in which only non-empty virtual output queues (VOQs) are served or all VOQs are served and is used to examine the effects of the RR scheduling schemes and various network parameters on the mean waiting time of packets. Quantitative examples demonstrate that properly balancing the reconfiguration frequency can effectively reduce the mean waiting time of packets