We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on ...

We consider the stability of robust scheduling policies for Lu-Kumar networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time in each group. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if...

This paper presents a general framework for optimal task reallocation in heterogeneous distributed computing systems (DCSs). The framework relies on a rigorous analytical model for the stochastic execution time of a workload. The model takes into account the heterogeneity and randomness of both service times and communication delays, an arbitrary task-reallocation policy as well as the stochast...

This paper concerns discrete-time queueing systems operating under a first-come-first-served queueing discipline, with deterministic service times of one slot and subject to independent server interruptions. We derive a relationship between the probability generating functions of the system contents during an arbitrary slot and of the system delay of an arbitrary customer. This relationship is ...

Faceted views over structured and semi structured data have been popular in user interfaces for some years. Deploying such views of arbitrary linked data at arbitrary scale has been hampered by lack of suitable back end technology. Many ontologies are also quite large, with hundreds of thousands of classes. Also, the linked data community has been concerned with the processing cost and potentia...

We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if it...

In this paper we consider M[X]/G(a, b)/1 queueing system with accessible service, server breakdown without interruption, multiple vacation and closedown time. The service rule is as follows: the server starts service only when a minimum number of customers ′a′ is available in the queue and the maximum service capacity is ′b′ units such that late entries are allowed to join a service batch, with...

We analyze D / G /1 and M / G /1 queues where the service time for an arrival depends on the amount of work in the system upon arrival. The models are motivated by the bit dropping methods (e.g., [12]) as a congestion control in broadband networks. The idea there is to reduce packet (cell) transmission time in case of congestion, while maintaining satisfactory quality of service. To study the l...

This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle.