Congestion Probabilities in Erlang-Engset Multirate Loss Models under the Multiple Fractional Channel Reservation Policy

Ioannis Moscholios

Abstract


A communication link that accommodates different service-classes whose
calls have different bandwidth requirements and compete for the available link bandwidth under the Multiple Fractional Channel Reservation (MFCR) policy is considered. The MFCR policy allows the reservation of real (not integer) number of channels in order to benefit calls of high channel (bandwidth) requirements. Two call arrival processes are studied: i) the Poisson (random) process and ii) the quasi-random process. In the first case, calls come from an infinite number of sources, while in the second case calls come from a finite number of sources. To determine call blocking probabilities for Poisson arriving calls, approximate but recursive formulas are proposed based on the notion of reverse transition rates. To determine time and call congestion probabilities for quasi-random arriving calls, approximate but recursive formulas are proved based on the fact that the proposed model does not have a product form solution for the steady state probabilities. The accuracy of the new formulas is verified through simulation and found to be highly satisfactory.

References


Akimaru, H.,. Kawashima, K. (1999). Teletraffic - Theory and Applications, 2nd edition, Springer, Berlin

Almasi, B., Bolch, G., Sztrik, J. (2004). Heterogeneous finite-source retrial queues, Journal of Mathematical Sciences, 121(5), 2590–2596

Alyatama, A. (2016). Computing the singlelink performance measurement for elastic optical OFDM, Photonic Network Communications, doi: 10.1007/s11107-016-0624-5

Alyatama, A. (2016). Calculation of the performance measurements for elastic optical OFDM networks, Photonic Network Communications, doi: 10.1007/s11107-016-0660-1

Cruz-Pérez, F., Vázquez-Ávila, J., OrtigozaGuerrero, L. (2004). Recurrent formulas for the multiple fractional channel reservation strategy in multiservice mobile cellular networks, IEEE Commun. Letters, 8(10), 629–631

Deng, Y., Prucnal, P. (2011). Performance analysis of heterogeneous optical CDMA networks with bursty traffic and variable power control, IEEE/OSA Journal of Optical Commun. Netw., 3(6), 487–492

Fodor, G., Telek, M. (2007). Bounding the Blocking Probabilities in Multirate CDMA Networks Supporting Elastic Services, IEEE/ACM Trans. Netw., 15(4), 944–956

Gharbi, N., Mokdad, L., Ben-Othman, J. (2015). A performance study of next generation cellular networks with base stations channels vacations, Proc. IEEE GLOBECOM, San Diego, USA

Glabowski, M., Kaliszan, A., Stasiak, M. (2008). Asymmetric convolution algorithm for blocking probability calculation in full-availability group with bandwidth reservation, IET Circuits, Devices & Systems, 2(1), 87–94

Glabowski, M., Kaliszan, A., Stasiak, M. (2016). Modelling overflow systems with distributed secondary resources, Computer Networks, vol. 108, 171–183

Glabowski, M., Sobieraj, M., Stasiak, M. (2009). Modelling limited-availability groups with BPP traffic and bandwidth reservation, Proc. 5th Advanced Int. Conf. Telecom. (AICT), Venice, Italy

Glabowski, M., Stasiak, M. (2002). Point-to-point blocking probability in switching networks with reservation, Annals of Telecommunications, 57(7-8), pp. 798–831

Glabowski, M., Stasiak, M. (2004). Multi-rate model of the limited availability group with finite source population, Proc. 10th Asia-Pacific Conf. on Commun., Beijing, China

Glabowski, M., Stasiak, M., Zwierzykowski, P. (2009). Modelling of virtual-circuit switching nodes with multicast connections, European Transactions on Telecommunications, 20(2), 123–137

Hanczewski, S., Kaliszan, A., Stasiak, M. (2016). Convolution model of a queueing system with the cFIFO service discipline, Mobile Information Systems, volume 2016, Article ID 2185714, 15 pages

Huang, Q., Ko, K-T., Iversen, V. (2008). Approximation of loss calculation for hierarchical networks with multiservice overflows, IEEE Trans. Commun., 56 (3), 466–473

Iversen, V., Benetis, V., Ha, N., Stepanov, S. (2004). Evaluation of Multi-service CDMA Networks with Soft Blocking, Proc. of ITC Specialist Seminar, Antwerp, Belgium

Kaufman, J. (1981). Blocking in a shared resourceenvironment, IEEE Trans. Commun. 29(10), 1474–1481

Kaufman, J. (1992). Blocking with retrials in a completely shared resource environment, Performance Evaluation, 15(2), pp. 99–113

Moscholios, I., Logothetis, M. (2010). The Erlang Multirate Loss Model with Batched Poisson Arrival Processes under the Bandwidth Reservation Policy, Computer Communications, 33(1), S167–S179

Moscholios, I., Logothetis, M., Kokkinakis, G. (2002). Connection Dependent Threshold Model: A Generalization of the Erlang Multiple Rate Loss Model, Performance Evaluation, 48(1-4), pp. 177–200

Moscholios, I., Logothetis, M., Koukias, M. (2006). A State-Dependent Multi-Rate Loss Model of Finite Sources with QoS Guarantee for Wireless Networks, Mediterranean Journal of Computers and Networks, 2(1), 10–20

Moscholios, I., Logothetis, M., Liokos, T. (2002). QoS Equalization in the Connection Dependent Threshold Model, Proc. CSNDSP, Staffordshire, U.K

Moscholios, I., Logothetis, M., Nikolaropoulos, P. (2005). Engset Multi-Rate State-Dependent Loss Models, Performance Evaluation, 59(2-3), 247–277

Moscholios, I., Logothetis, M., Vardakas, J., Boucouvalas, A. (2015). Performance metrics of a multirate resource sharing teletraffic model with finite sources under the threshold and bandwidth reservation policies, IET Networks, 4(3), 195–208

Moscholios, I., Nikolaropoulos, P., Logothetis, M. (2003). Call level blocking of ON-OFF traffic sources with retrials under the complete sharing policy, Proc. of 18th ITC, Berlin, Germany

Renard, B., Elayoubi, S., Simonian, A. (2012). A dimensioning method for the LTE X2 interface, Proc. IEEE WCNC, Shanghai, China

Roberts, J. (1981). A service system with heterogeneous user requirements, in: G. Pujolle (Ed.), Performance of Data Communications systems and their applications, North Holland, Amsterdam, pp. 423–431

Roberts, J. (1983). Teletraffic models for the Telecom 1 Integrated Services Network, Proc. 10th ITC, paper 1.1–2, Montreal

Simscript III, http://www.simscript.com (last accessed: Dec. 2016)

Stasiak, M., Glabowski, M. (2000). A simple approximation of the link model with reservation by a one-dimensional Markov chain, Performance Evaluation, 41(2-3), pp. 195–208

Stasiak, M., Glabowski, M., Wisniewski, A., Zwierzykowski, P. (2011). Modeling and Dimensioning of Mobile Networks, Wiley

Stamatelos, G., Hayes, J. (1994). Admission control techniques with application to broadband networks, Comput. Commun., 17(9), pp. 663–673

Stamatelos, G., Koukoulidis, V. (1997). Reservation-Based Bandwidth Allocation in a Radio ATM Network, IEEE/ACM Trans. Netw., 5(3), pp. 420–428

Stasiak, M., Parniewicz, D., Zwierzykowski, P. (2013). Traffic Engineering for Multicast Connections in Multiservice Cellular Network, IEEE Transactions on Industrial Informatics, 9(1), 262–270

Stasiak, M., Sobieraj, M., Weissenberg, J., Zwierzykowski, P. (2012). Analytical Model of the Single Threshold Mechanism with Hysteresis for Multi-service Networks, IEICE Transactions on Communications, E95-B(1), 120–132

Stasiak, M., Zwierzykowski, P., Parniewicz, D. (2009). Modelling of the WCDMA interface in the UMTS network with Soft Handoff Mechanism, Proc. IEEE GLOBECOM, Hawaii, Honolulu

Vassilakis, V., Kallos, G., Moscholios, I., Logothetis, M. (2008). Call-Level Analysis of W-CDMA Networks Supporting Elastic Services of Finite Population, IEEE ICC 2008, Beijing, China

Vassilakis, V., Moscholios, I., Logothetis, M. (2008). Call-level performance modelling of elastic and adaptive service-classes with finite population, IEICE Trans. Commun., E91-B(1), 151–163

Vassilakis, V., Moscholios, I., Logothetis, M. (2012). The Extended Connection-Dependent Threshold Model for Call-level Performance Analysis of Multi-rate Loss Systems under the Bandwidth Reservation Policy, Int. Journal of Communication Systems, 25(7), 849–873 [41] Vardakas, J., Moscholios, I., Logothetis, M., Stylianakis, V. (2011). An Analytical Approach for Dynamic Wavelength Allocation in WDM-TDMA PONs Servicing ON-OFF Traffic, IEEE/OSA Journal of Optical Commun. Netw., 3(4), 347–358

Vardakas, J., Moscholios, I., Logothetis, M., Stylianakis, V. (2012). On Code reservation in Multi-rate OCDMA Passive Optical Networks, Proc. IEEE/IET CSNDSP, Poznan, Poland

Vardakas, J., Moscholios, I., Logothetis, M., Stylianakis, V. (2013). Performance Analysis of OCDMA PONs Supporting Multi-Rate Bursty Traffic, IEEE Trans. Commun., 61(8), 3374–3384

Vassilakis, V., Moscholios, I., Vardakas, J., Logothetis, M. (2014). Handoff Modeling in Cellular CDMA with Finite Sources and State-Dependent Bandwidth Requirements, Proc. of IEEE CAMAD, Athens, Greece

Wang, Z., Mathiopoulos, P., Schober, R. (2008). Performance Analysis and Improvement Methods for Channel Resource Management Strategies of LEOMSS with Multiparty Traffic, IEEE Trans. Vehicular Tech., 57(6), 3832–3842

Wang, Z., Mathiopoulos, P., Schober, R. (2009). Channel partitioning policies for multi-class traffic in LEO-MSS, IEEE Trans. Aerosp. Electron. Syst., 45(4), 1320–1334

Widjaja I., Roche, H. (2009). Sizing X2 bandwidth for Inter-connected eNBs, Proc. IEEE VTC-Fall, Anchorage, Alaska, USA

Zhang, F., Wang, J. (2013). Performance analysis of the retrial queues with finite number of sources and service interruptions, Journal of the Korean Statistical Society, 42(1), 117–131


Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 IMAGE PROCESSING & COMMUNICATIONS