4,200 research outputs found
Analysis of the finite-source multiclass priority queue with an unreliable server and setup time
In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model
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Analysis of a class of distributed queues with application
Recently we have developed a class of media access control algorithms for different types of Local Area Networks. A common feature of these LAN algorithms is that they represent various strategies by which the processors in the LAN can simulate the availability of a centralized packet transport facility, but whose service incorporates a particular type of change over time known as 'moving sever' overhead. First we describe the operation of moving server systems in general, for both First-Come - First-Served and Head-of-the-Line orders of service, together with an approach for their delay analysis in which we transform the moving server queueing system into a conventional queueing system having proportional waiting times. Then we describe how the various LAN algorithms may be obtained from the ideal moving server system, and how a significant component of their performance characteristics is determined by the performance characteristics of that ideal system. Finally, we evaluate the compatibility of such LAN algorithms with separable queueing network models of distributed systems by computing the interdeparture time distribution for M/M/1 in the presence of moving server overhead. Although it is not exponential, except in the limits of low server utilization or low overhead, the interdeparture time distribution is a weighted sum of exponential terms with a coefficient of variation not much smaller than unity. Thus, we conjecture that a service centre with moving server overhead could be used to represent one of these LAN algorithms in a product form queueing network model of a distributed system without introducing significant approximation errors
Queue-length balance equations in multiclass multiserver queues and their generalizations
A classical result for the steady-state queue-length distribution of
single-class queueing systems is the following: the distribution of the queue
length just before an arrival epoch equals the distribution of the queue length
just after a departure epoch. The constraint for this result to be valid is
that arrivals, and also service completions, with probability one occur
individually, i.e., not in batches. We show that it is easy to write down
somewhat similar balance equations for {\em multidimensional} queue-length
processes for a quite general network of multiclass multiserver queues. We
formally derive those balance equations under a general framework. They are
called distributional relationships, and are obtained for any external arrival
process and state dependent routing as long as certain stationarity conditions
are satisfied and external arrivals and service completions do not
simultaneously occur. We demonstrate the use of these balance equations, in
combination with PASTA, by (i) providing very simple derivations of some known
results for polling systems, and (ii) obtaining new results for some queueing
systems with priorities. We also extend the distributional relationships for a
non-stationary framework
Product-form solutions for integrated services packet networks and cloud computing systems
We iteratively derive the product-form solutions of stationary distributions
of priority multiclass queueing networks with multi-sever stations. The
networks are Markovian with exponential interarrival and service time
distributions. These solutions can be used to conduct performance analysis or
as comparison criteria for approximation and simulation studies of large scale
networks with multi-processor shared-memory switches and cloud computing
systems with parallel-server stations. Numerical comparisons with existing
Brownian approximating model are provided to indicate the effectiveness of our
algorithm.Comment: 26 pages, 3 figures, short conference version is reported at MICAI
200
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