@article{goodman:singleuser:1996,
author = “David J. Goodman and P. Krishnan and Binay Sugla”,
title = “Minimizing Queuing Delays and Number of Messages in Mobile Phone Location”,
journal = “Mobile Networks and Applications”,
volume = “1″,
number = “1″,
pages = “39-48″,
year = “1996″,
url = “citeseer.ist.psu.edu/20574.html” }
Minimizing Queuing Delays and Number of Messages in Mobile Phone Location
In this paper, Goodman et. al made two contributations.
First, they established a model of paging a single mobile user in $N$ cells within $D$ rounds. They assume $p_1=\ldots=p_N=\frac{1}{N}$ and paging strategy is to arbitrarily partition the cells into equal-sized subsets. The also assumes the calls arrives at Poisson distribution and the bottle neck of the paging process is at the radio channels. They construct the $M/M/1$ model, that is, multiple calls arrives at multiple users, while only a single user sent by a single call can be paged at a time. Through analysis, they established the distribution of the queue length in while calls are waiting to page.
Second, they designed an algorithm, of complexity $\Theta(N^2 D)$, using dynamical program, such that a paging strategy can be generated through the $p_i$s and the expected number of paged cells is minimized.
