Modeling user impatience and its impact on performance in mobile networks

We study in this work user impatience and quantify its impact on the performance of mobile networks, notably LTE networks, in the presence of data flows experiencing heterogeneous radio conditions. We consider a dynamic user setting where users come to the system at different time instants and leave it after a finite duration, either after completion of their data transfers or earlier, at the expiry of some patience duration. We derive closed-form analytical expressions for the system stationary probability distribution, in general and for some particular distributions for the impatience duration and file size, and obtain several performance metrics such as system load and mean transfer times, taking into account the heterogeneity of users locations in the cell. Our numerical results quantify these metrics, as a function of the impatience rate, as well as the traffic region where the impatience impact becomes preponderant.

[1]  Alain Jean-Marie,et al.  Illustrated review of convergence conditions of the value iteration algorithm and the rolling horizon procedure for average-cost MDPs , 2012, Ann. Oper. Res..

[2]  J.-C. Cano,et al.  Modeling of mobility and groups in inter-vehicular MANET-based networks , 2007, 2007 2nd International Symposium on Wireless Pervasive Computing.

[3]  J. Michael Harrison,et al.  Dynamic Control of a Queue with Adjustable Service Rate , 2001, Oper. Res..

[4]  Søren Asmussen,et al.  Ruin probabilities , 2001, Advanced series on statistical science and applied probability.

[5]  Philippe Robert,et al.  Heavy tailed M/G/1-PS queues with impatience and admission control in packet networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[6]  Ward Whitt,et al.  Deciding Which Queue to Join: Some Counterexamples , 1986, Oper. Res..

[7]  Mohamed Kadhem Karray,et al.  Analytical evaluation of QoS in the downlink of OFDMA wireless cellular networks serving streaming and elastic traffic , 2010, IEEE Transactions on Wireless Communications.

[8]  Philip Kibet Langat,et al.  Femtocell Cluster-Based Mobility-Aware Resource Allocation Scheme for OFDMA Network , 2014 .

[9]  D. J. White.  An Example of Loosely Coupled Stages in Dynamic Programming , 1973 .

[10]  Peter W. Glynn,et al.  A Diffusion Approximation for a Markovian Queue with Reneging , 2003, Queueing Syst. Theory Appl..

[11]  Sem C. Borst,et al.  Capacity of Wireless Data Networks with Intra- and Inter-Cell Mobility , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[12]  F. Baccelli,et al.  Single-server queues with impatient customers , 1984, Advances in Applied Probability.

[14]  Shaler Stidham,et al.  Individual versus Social Optimization in Exponential Congestion Systems , 1977, Oper. Res..

[15]  Chris Blondia,et al.  Classifying Users Based on Their Mobility Behaviour in LTE Networks , 2014, ICWMC 2014.

[16]  David W. Low,et al.  Optimal Dynamic Pricing Policies for an M/M/s Queue , 1974, Oper. Res..

[17]  Thomas Bonald,et al.  A Flow-Level Performance Model for Mobile Networks Carrying Adaptive Streaming Traffic , 2014, 2015 IEEE Global Communications Conference (GLOBECOM).

[18]  Baris Ata,et al.  Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates , 2006, Manag. Sci..

[19]  Thomas Bonald,et al.  A Flow-Level Performance Model for Mobile Networks Carrying Adaptive Streaming Traffic , 2014, GLOBECOM 2014.

[20]  Seungjoon Lee,et al.  Abandonment and its impact on P2P VoD streaming , 2013, IEEE P2P 2013 Proceedings.

[21]  Matti Siekkinen,et al.  Using crowd-sourced viewing statistics to save energy in wireless video streaming , 2013, MobiCom.

[22]  Victor C. M. Leung,et al.  Capacity Planning for Group-Mobility Users in OFDMA Wireless Networks , 2006, EURASIP J. Wirel. Commun. Netw..

[23]  Philippe Robert,et al.  The impact of reneging in processor sharing queues , 2006, SIGMETRICS '06/Performance '06.

[24]  M. Miyazawa,et al.  The basic equations for a supplemented GSMP and its applications to queues , 1988, Journal of Applied Probability.

[25]  Haim Mendelson,et al.  Controlling the GI/M/1 queue by conditional acceptance of customers , 1981 .

[26]  Raj Kumar Samanta,et al.  Performance Analysis of Cellular Wireless Network by Queuing Priority Handoff calls , 2009 .

[27]  Steven Nahmias.  Queues with Impatient Customers , 2011 .

[28]  Thomas Bonald,et al.  Wireless downlink data channels , 2003 .

[29]  Zhen Liu,et al.  Capacity, delay and mobility in wireless ad-hoc networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[30]  Christian Bettstetter,et al.  Mobility modeling in wireless networks: categorization, smooth movement, and border effects , 2001, MOCO.

[31]  Hossam S. Hassanein,et al.  Towards mobility-aware predictive radio access: modeling; simulation; and evaluation in LTE networks , 2014, MSWiM '14.

[32]  Eitan Altman,et al.  Impact of flow-level dynamics on QoE of video streaming in wireless networks , 2013, 2013 Proceedings IEEE INFOCOM.

[33]  Robert E. Stanford,et al.  Reneging Phenomena in Single Channel Queues , 1979, Math. Oper. Res..

[34]  Ramesh K. Sitaraman,et al.  Network performance: Does it really matter to users and by how much? , 2013, 2013 Fifth International Conference on Communication Systems and Networks (COMSNETS).

[35]  A. Mandelbaum,et al.  Optimal Entering Rules for a Customer with Wait Option at an M/G/1 Queue , 1983 .

[36]  D. Y. Barrer.  Queuing with Impatient Customers and Ordered Service , 1957 .

[37]  Eitan Altman,et al.  Probabilistic analysis of buffer starvation in Markovian queues , 2011, 2012 Proceedings IEEE INFOCOM.

[38]  Rein Nobel,et al.  A discrete-time queueing model with abandonments , 2010 .

[39]  Lusheng Ji,et al.  Understanding the impact of network dynamics on mobile video user engagement , 2014, SIGMETRICS '14.

[40]  Kishor S. Trivedi,et al.  Analytic modeling of handoffs in wireless cellular networks , 2002, Inf. Sci..

[41]  Shuanming Li,et al.  On the probability of ruin in a Markov-modulated risk model , 2005 .

[42]  Wei Song,et al.  Performance Analysis of Probabilistic Multipath Transmission of Video Streaming Traffic over Multi-Radio Wireless Devices , 2012, IEEE Transactions on Wireless Communications.

[43]  Onésimo Hernández-Lerma,et al.  Fatou's Lemma and Lebesgue's convergence theorem for measures , 2000 .

[44]  David Tse,et al.  Mobility increases the capacity of ad hoc wireless networks , 2002, TNET.

[45]  Hamid R. Rabiee,et al.  Mobility pattern recognition in mobile ad-hoc networks , 2007, Mobility '07.

[46]  Jorma T. Virtamo,et al.  Dispatching problem with fixed size jobs and processor sharing discipline , 2011, 2011 23rd International Teletraffic Congress (ITC).

[47]  Matthew J. Sobel.  Making Short-Run Changes in Production when the Employment Level is Fixed , 1970, Oper. Res..

[48]  Ramesh K. Sitaraman,et al.  Video Stream Quality Impacts Viewer Behavior: Inferring Causality Using Quasi-Experimental Designs , 2012, IEEE/ACM Transactions on Networking.

[49]  Salah-Eddine Elayoubi,et al.  Performance Evaluation of Cellular Networks Offering TV Services , 2011, IEEE Transactions on Vehicular Technology.

[50]  Philippe Robert,et al.  Fluid Limits for Processor-Sharing Queues with Impatience , 2008, Math. Oper. Res..

[51]  Uri Yechiali,et al.  Queues with slow servers and impatient customers , 2010, Eur. J. Oper. Res..

[52]  Sem C. Borst,et al.  How mobility impacts the flow-level performance of wireless data systems , 2004, IEEE INFOCOM 2004.

[53]  Tong Liu,et al.  Mobility modeling, location tracking, and trajectory prediction in wireless ATM networks , 1998, IEEE J. Sel. Areas Commun..

[54]  N. Gautam,et al.  Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters , 2009, 0911.2436.

[55]  Constantinos Maglaras,et al.  Pricing and Capacity Sizing for Systems with Shared Resources: Approximate Solutions and Scaling Relations , 2003, Manag. Sci..

[56]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[57]  Thomas Bonald,et al.  Congestion at flow level and the impact of user behaviour , 2003, Comput. Networks.

[58]  Gustavo de Veciana,et al.  Bandwidth sharing: the role of user impatience , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[59]  Avishai Mandelbaum,et al.  Designing a Call Center with Impatient Customers , 2002, Manuf. Serv. Oper. Manag..

[60]  Mostafa H. Ammar,et al.  Network-layer fairness for adaptive video streams , 2015, 2015 IFIP Networking Conference (IFIP Networking).

[61]  Gustavo de Veciana,et al.  Flow-level QoS for a dynamic load of rate adaptive sessions sharing a bottleneck link , 2007, Comput. Networks.

[62]  Vyas Sekar,et al.  Understanding the impact of video quality on user engagement , 2011, SIGCOMM.