Abstract
Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte‐Carlo simulations are used to supplement our analytical results.
Highlights
Point processes have been used to describe spatial distribution of nodes in wireless networks
We corroborate our theoretical results through numerical examples
Since the number of base stations (BSs) is smaller than the number of mobile stations (MSs) in general, we choose the smaller value of λB for BSs than λM for MSs
Summary
Point processes have been used to describe spatial distribution of nodes in wireless networks. In the case of cognitive radio networks, locations of primary and secondary users have been modeled as point processes [11,12,13,14]. Stochastic ordering of point processes provides an ideal framework for comparing two deployment/usage scenarios even in cases where the performance metrics cannot be computed in closed form. These partial orders capture intuitive notions like one point process being more dense or more variable. Existing works on point process modeling for wireless networks have paid little attention to how two intractable scenarios can be compared to aid in system optimization
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 callDisclaimer: 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.
