Abstract
This paper considers a fork-join network with a group of heterogeneous servers in each service station, e.g. servers having different service rate. The main research interests are the properties of such fork-join networks in equilibrium, such as distributions of response times, maximum queue lengths and load carried by servers. This paper uses exact Monte-Carlo simulation methods to estimate the characteristics of heterogeneous fork-join networks in equilibrium, for which no explicit formulas are available. The algorithm developed is based on coupling from the past. The efficiency of the sampling algorithm is shown theoretically and via simulation.
Highlights
This paper considers a fork-join network with a group of heterogeneous servers in each service station, e.g. servers having different service rate
The main research interests are the properties of such fork-join networks in equilibrium, such as distributions of response times, maximum queue lengths and load carried by servers
A fork-join network consists of K parallel service stations, where each incoming job is split into K subtasks at the fork station and processed separately in each service station
Summary
A fork-join network consists of K parallel service stations, where each incoming job is split into K subtasks at the fork station and processed separately in each service station. For more general forkjoin networks with homogeneous service, existing methods focus on finding approximations or bounds of mean response times and approximations of maximum queue-length distributions with N = ∞ (infinite waiting capacity), such as Nelson and Tantawi (1988), Baccelli et al (1989), Balsoma et al (1998), Raghavan and Viswanadham (2001) and Ko and Serfozo (2004). Dai (2011) considers the use of exact Monte Carlo simulations, based on coupling from the past (CFTP) (Propp and Wilson, 1996), to estimate the distributions of response time and queue length for homogeneous fork-join networks with N < ∞. The other advantage of the exact Monte Carlo simulation methods is that it can provide empirical distribution estimates for response time and maximum queue length.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Statistics and Probability
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
