Modeling cellular network traffic with mobile call graph constraints

Junwhan Kim, V. S. Anil Kumar, Achla Marathe, Guanhong Pei, Sudip Saha, Balaaji S.P. Subbiah
2011 Proceedings of the 2011 Winter Simulation Conference (WSC)  
The design, analysis and evaluation of protocols in cellular and hybrid networks requires realistic traffic modeling, since the underlying mobility and traffic model has a significant impact on the performance. We present a unified framework involving constrained temporal graphs that incorporate a variety of spatial, homophily and call-graph constraints into the network traffic model. The specific classes of constraints include bounds on the number of calls in given spatial regions, specific
more » ... ophily relations between callers and callees, and the indegree and outdegree distributions of the call graph, for the whole time duration and intervals. Our framework allows us to capture a variety of complex behavioral adaptations and study their impacts on the network traffic. We illustrate this by a case study showing the impact of different homophily relations on the spatial and temporal characteristics of network traffic as well as the structure of the call graphs. 3170 978-1-4577-2109-0/11/$26.00 ©2011 IEEE Kim, Kumar, Marathe, Pei, Saha, and Subbiah first-principles approaches for synthetic network traffic modeling, which integrate a number of different data sets, and match aggregate properties, such as the known call arrival rate and call duration distributions. In most applications, modeling network traffic to match known aggregate distributions is not adequate. User behavior changes in response to new wireless technologies, changes in pricing and new incentives by providers and emergency and disaster situations. For instance, the increased data traffic by iPhone users caused severe strain on AT&T's infrastructure. Barrett et al. (Barrett, Beckman, Channakeshava, Huang, Kumar, Marathe, Marathe, and Pei 2010) model the changes in calling behavior during an evacuation, and show that this leads to a significant strain on the communication network. An important aspect of user behavior in such settings is "homophily", which implies specific correlations between callers and callees. For instance, (Beckman, Channakeshava, Huang, Kumar, Marathe, Marathe, and Pei 2010a),(Kroc, Eidenbenz, and Smith 2009) use location based homophily to specify call patterns, in which people who are co-located during their activities in a day have a higher likelihood of calling each other. There can be other kinds of homophilies, e.g., age-based, in which people are more likely to call others in the same age group (Jackson 2008). Data for such homophily relations is likely to be even more challenging to obtain, because of the obvious privacy issues. Aggregate statistical properties related to this have been studied in the form of the "call graph", which has one or more edges between people who participate in a call. Seshadri et al. (Seshadri, Machiraju, Sridharan, Bolot, Faloutsos, and Leskove 2008) use data on a long time scale from the Sprint network and compute properties such as the degree distribution of the call graph. Nanavati et al. (Nanavati, Singh, Chakraborty, Dasgupta, Mukherjee, Gurumurthy, and Joshi 2008) study other properties besides the degree, such as the diameter, cores and cliques. The degree distribution of call graphs and indegree-outdegree correlations show that they are not Poisson, and have several properties similar to the web-graph. Realistic modeling of network traffic requires preserving both aggregate traffic characteristics (e.g., arrival rates), as well as the call graph properties. We are not aware of any simulation framework that captures all these aspects, and is the motivation for our work. In this paper, we develop a unified framework involving constrained temporal graphs that incorporates a variety of spatial, homophily and call-graph constraints into the network traffic model. Our main contributions are summarized below. (1). Unified dynamic graph framework for spatial and homophily relations: We develop a unified framework that satisfies traffic properties as well as spatial, homophily based and call-graph based constraints. The specific classes of constraints we incorporate include: (i) bounds on the number of calls in given spatial regions -this captures, e.g., base station capacity constraints, which limit how many calls can be made in a base station cell, (ii) specific homophily relations between callers and callees, e.g., between age groups or other demographic classes, (iii) constraints on the indegree and outdegree distributions of the call graph, for the whole time duration, as well as for specific time intervals. We show that these constraints can be viewed in terms of degree constraints for different subsets in the dynamic call graph, which gives a general approach to formulate them. We extend the session generation module in (Beckman, Channakeshava, Huang, Kumar, Marathe, Marathe, and Pei 2010a) to incorporate these features -incorporating these constraints requires extending this framework to use and keep track of location and demographic information for the population. (2). Illustrative case study: our extended framework allows us to capture a variety of complex behavioral adaptations and study their impacts on the network traffic. We illustrate this by a case study showing the impact of different homophily relations on the spatial and temporal characteristics of network traffic as well as the structure of the call graphs. The remainder of the paper is organized in the following manner. In Section 2, we give a brief overview of traffic characteristics and SSRSM. In Section 3, we discuss traffic and call constraints. We describes our algorithm and implementation in Section 4. Our results are discussed in Section 5.
doi:10.1109/wsc.2011.6148015 dblp:conf/wsc/KimKMPSS11 fatcat:ozmsd3qm7rafnf4hndt432glve