In this paper, we present a discrete-time single-server finite-buffer queue in which the server takes single/multiple vacations whenever the system becomes empty. The interarrival times are geometrically distributed and service, vacation times are independently identically distributed random variables and their durations are integral multiples of a slot duration. We obtain the state probabiliti...

1 Q I − − ) ( y , where the j th entry of the row vector y is the probability that the system state seen by the first arrival during a busy period is j and 1 Q I − − ) ( is the fundamental matrix associated with the standard GI/M/1 queue. In this paper, we present the entries of 1 Q I − − ) ( explicitly. Also, we illustrate how to find y by examples such as the N -policy GI/M/1 queue with or wi...

This paper considers a discrete-time Geo/G/1 queue with multiple adaptive vacations and variable input rate. The main purpose of this paper is to present a queuelength analysis of this system. Using a new analytic method, the late arrival system with delayed access (LAS-DA) and the early arrival system (EAS), have been examined. For both the cases, We derive the recursive solution for queue len...

We use the Method of Collective Marks to analyze some time-dependent processes in the M/G/1 queue with single and multiple vacations. With the server state specified at a fixed time t > 0, the Laplace transforms with respect to t of mixed transforms for the joint distribution of the number of departures by time t, the queue length, the virtual waiting time, the elapsed and remaining service/vac...

CONTEXT Many clinical disciplines report high rates of burnout, which lead to low quality of care. Palliative care clinicians routinely manage patients with significant suffering, aiming to improve quality of life. As a major role of palliative care clinicians involves educating patients and caregivers regarding identifying priorities and balancing stress, we wondered how clinician self-managem...

We study a system with unlimited service potential where all service requests are served in parallel. The entire system itself becomes unavailable for a random period of time at the first instance that the system becomes idle. A queue builds up while the system is unavailable, and then all waiting customers enter the system simultaneously-each to its own processor-when the system becomes availa...

Various magnetic resonance (MR) techniques are used to study the pathological evolution of demyelinating diseases, such as multiple sclerosis (MS). However, few studies have validated MR derived measurements with histopathology. Here, we determine the correlation of myelin water imaging, an MR measure of myelin content, with quantitative histopathologic measures of myelin density. The multi-com...