A Matrix-Analytic Solution for Randomized Load Balancing Models with PH Service Times
نویسندگان
چکیده
In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as supermarket models) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We describe the supermarket model as a system of differential vector equations, provide a doubly exponential solution to the fixed point of the system of differential vector equations, and analyze the exponential convergence of the current location of the supermarket model to its fixed point.
منابع مشابه
A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times
In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as supermarket models) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literat...
متن کاملDoubly Exponential Solution for Randomized Load Balancing Models with Markovian Arrival Processes and PH Service Times
In this paper, we provide a novel matrix-analytic approach for studying doubly exponential solutions of randomized load balancing models (also known as supermarket models) with Markovian arrival processes (MAPs) and phase-type (PH) service times. We describe the supermarket model as a system of differential vector equations by means of density dependent jump Markov processes, and obtain a close...
متن کاملDoubly Exponential Solution for Randomized Load Balancing Models with General Service Times
The randomized load balancing model (also called supermarket model) is now being applied to the study of load balancing in data centers and multi-core servers systems. It is very interesting to analyze the general service times in the supermarket model, and specifically understand influence of the heavy-tailed service times on the doubly exponential solution. Since the supermarket model is a co...
متن کاملAnalysis of two production inventory systems with buffer, retrials and different production rates
This paper considers the comparison of two ðs; SÞ production inventory systems with retrials of unsatisfied customers. The time for producing and adding each item to the inventory is exponentially distributed with rate b. However, a production rate ab higher than b is used at the beginning of the production. The higher production rate will reduce customers’ loss when inventory level appro...
متن کاملRandomized load balancing in heavy tra c
We consider three randomized schemes for load balancing among a xed number, N , of resources, and analyze them in the heavy tra c limit. The rst is join the shortest queue, where arrivals are routed to the shortest among d randomly chosen queues, where d ∈ {2, . . . , N}. The second is redundancy routing, where jobs are replicated d times, routed simultaneously to d randomly chosen queues, and ...
متن کامل