We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

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The paper deals with batch service queues with vacations in which customers arrive according to a Poisson process. Decomposition method is used to derive the queue length distributions both for single and multiple vacation cases. The authors look at other decomposition techniques and discuss some related open problems

At the extremes of the complexity‐performance plane, there are two exemplary QoS management architectures: Integrated Services (IntServ) and Differentiated Services (DiffServ). IntServ performs ideally but is not scalable. DiffServ is simple enough to be adopted in today's core networks, but without any performance guarantee. Many compromise solutions have been proposed. These schemes, called quasi‐stateful IntServ or stateful DiffServ, however, have not attracted much attention due to their inherently compromising natures. Two disruptive flow‐based architectures have been recently introduced: the flow‐aware network (FAN) and the flow‐state‐aware network (FSA). FAN's control is implicit without any signaling. FSA's control is even more sophisticated than that of IntServ. In this paper, we survey established QoS architectures, review disruptive architectures, discuss their rationales, and points out their disadvantages. A new QoS management architecture, flow‐aggregate‐based services (FAbS), is then proposed. The FAbS architecture has two novel building blocks: inter‐domain flow aggregation and endpoint implicit admission control.

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Many control schemes have been proposed for flow‐level traffic control. However, flow‐level traffic control is implemented only in limited areas such as traffic monitoring and traffic control at edge nodes. No clear solution for end‐to‐end architecture has been proposed. Scalability and the lack of a business model are major problems for deploying end‐to‐end flow‐level control architecture. This paper introduces an end‐to‐end transport architecture and a scalable control mechanism to support the various flow‐level QoS requests from applications.