Batch processor sharing with hyper-exponential service time
نویسنده
چکیده
We study the Processor-Sharing queueing model with a hyper-exponential service time distribution and Poisson batch arrival process. In the case of the hyperexponential service time distribution we find an analytical expression for the expected conditional response time function and obtain an alternative proof of its concavity with respect to the service time.
منابع مشابه
Batch Arrival Processor-Sharing with Application to Multi-Level Processor-Sharing Scheduling
We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping principle, we demonstrate the existence and uniqueness of a solution to the integral equation. Then we provide asymptotical analysis as well as tight bounds for the expected response time conditioned on the service time....
متن کاملA Gated Processor - Sharing M / G / 1 Queue with Limited Number of Service Positions
In this note, we consider a single server queue with gated processor-sharing discipline. Customers arrive according to a Poisson process with rate A and service times are independent and identically distributed (i.i.d.) as an arbitrary random variable S with distribution function H(t) and LST H(s). In the gated processor-sharing discipline, when an arriving customer finds the queue empty, he is...
متن کاملConcavity of the conditional mean sojourn time in the M/G/1 processor-sharing queue with batch arrivals
For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.
متن کاملEstimating mean sojourn time in the processor sharing M/G/1 queue with inaccurate job size information
We seek to approximate the mean sojourn time in the processor sharing M/G/1 queue with inaccurate job size information. Suppose we are given the arrival rate λ and random service time Ŝ = SX where X ∼ LN(0, σ) represents the inaccuracy. Denote the mean sojourn time in an M/G/1 queue with processor sharing with service time Ŝ by E(T̂) and with service time S by E(T). Finally, E(T̂) denotes the mea...
متن کاملOn the Sojourn times for Many-queue Head-of-the-line Processor-sharing Systems with Permanent Customers on the Sojourn times for Many-queue Head-of-the-line Processor-sharing Systems with Permanent Customers 1
We consider a single server system consisting of n queues with diierent types of customers (Poisson streams) and k permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). The stability condition and a pseudo work conservation law will be given for arbitrary service time distrib...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Oper. Res. Lett.
دوره 36 شماره
صفحات -
تاریخ انتشار 2008