Management of a shared-spectrum network in wireless communications. (English) Zbl 1443.90147
Summary: We consider a band of the electromagnetic spectrum with a finite number of identical channels shared by both licensed and unlicensed users. Such a network differs from most many-server, two-class queues in service systems, including call centers, because of the restrictions imposed on the unlicensed users to limit interference to the licensed users. We first approximate the key performance indicators – namely the throughput rate of the system and the delay probability of the licensed users under the asymptotic regime, which requires the analysis of both scaled and unscaled processes simultaneously using the averaging principle. Our analysis reveals a number of distinctive properties of the system. For example, sharing does not affect the level of service provided to the licensed users in an asymptotic sense even when the system is critically loaded. We then study the optimal sharing decisions of the system to maximize the system throughput rate while maintaining the delay probability of the licensed users below a certain level when the system is overloaded. Finally, we extend our study to systems with time-varying arrival rates and propose a diffusion approximation to complement our fluid one.
The e-companion is available at https://doi.org/10.1287/opre.2017.1707.
The e-companion is available at https://doi.org/10.1287/opre.2017.1707.
MSC:
| 90B18 | Communication networks in operations research |
| 90B22 | Queues and service in operations research |
| 60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
References:
| [1] | Akyildiz IF, Lee W-Y, Vuran MC, Mohanty S (2006) Next generation/dynamic spectrum access/cognitive radio wireless networks: A survey. Comput. Networks 50(13):2127-2159.Crossref, Google Scholar · Zbl 1107.68018 · doi:10.1016/j.comnet.2006.05.001 |
| [2] | Artalejo J, Gómez-Corral A (2008) Retrial Queueing Systems: A Computational Approach (Springer, Berlin).Crossref, Google Scholar · Zbl 1161.60033 · doi:10.1007/978-3-540-78725-9 |
| [3] | Atar R, Mandelbaum A, Reiman MI (2004) Scheduling a multi class queue with many exponential servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 14(3):1084-1134.Crossref, Google Scholar · Zbl 1049.60079 · doi:10.1214/105051604000000233 |
| [4] | Bansal G, Hossain J, Bhargava V (2008) Optimal and suboptimal power allocation schemes for OFDM-based cognitive radio systems. IEEE Trans. Wireless Comm. 7(11):4710-4718.Crossref, Google Scholar · doi:10.1109/T-WC.2008.07091 |
| [5] | Biglieri E, Goldsmith A, Greenstein L, Mandayam N, Poor H (2013) Principles of Cognitive Radio (Cambridge University Press, New York).Google Scholar |
| [6] | Brosh I (1969) Preemptive priority assignment in multichannel systems. Oper. Res. 17(3):526-535.Link, Google Scholar · Zbl 0172.21804 |
| [7] | Buzen JP, Bondi AB (1983) The response times of priority classes under preemptive resume in M/M/m queues. Oper. Res. 31(3):456-465.Link, Google Scholar · Zbl 0514.90027 |
| [8] | Capar F, Martoyo I, Weiss T, Jondral F (2002) Comparison of bandwidth utilization for controlled and uncontrolled channel assignment in a spectrum pooling system. IEEE 55th Vehicular Tech. Conf., Vol. 3 (IEEE, Piscataway, NJ), 1069-1073.Google Scholar |
| [9] | de Véricourt F, Jennings OB (2008) Dimensioning large-scale membership services. Oper. Res. 56(1):173-187.Link, Google Scholar · Zbl 1167.90447 |
| [10] | de Véricourt F, Zhou Y-P (2005) Managing response time in a call-routing problem with service failure. Oper. Res. 53(6):968-981.Link, Google Scholar · Zbl 1165.90417 |
| [11] | Devroye N, Mitran P, Tarokh V (2006) Achievable rates in cognitive radio channels. IEEE Trans. Inform. Theory 52(5):1813-1827.Crossref, Google Scholar · Zbl 1293.94012 · doi:10.1109/TIT.2006.872971 |
| [12] | El Gamal A, Mammen J, Prabhakar B, Shah D (2006) Optimal throughput-delay scaling in wireless networks—Part I: The fluid model. IEEE Trans. Inform. Theory 52(6):2568-2592.Crossref, Google Scholar · Zbl 1300.94004 · doi:10.1109/TIT.2006.874379 |
| [13] | Falin GI, Templeton JGC (1997) Retrial Queues, Vol. 75 (CRC Press, Boca Raton, FL).Crossref, Google Scholar · doi:10.1007/978-1-4899-2977-8 |
| [14] | Goldsmith A, Jafar S, Maric I, Srinivasa S (2009) Breaking spectrum gridlock with cognitive radios: An information theoretic perspective. Proc. IEEE 97(5):894-914.Crossref, Google Scholar · doi:10.1109/JPROC.2009.2015717 |
| [15] | Gong S, Wang P, Duan L (2015) Distributed power control with robust protection for PUs in cognitive radio networks. IEEE Trans. Wireless Comm. 14(6):3247-3258.Crossref, Google Scholar · doi:10.1109/TWC.2015.2403357 |
| [16] | Gupta P, Kumar P (2000) The capacity of wireless networks. IEEE Trans. Inform. Theory 46(2):388-404.Crossref, Google Scholar · Zbl 0991.90511 · doi:10.1109/18.825799 |
| [17] | Gurvich I, Perry O (2012) Overflow networks: Approximations and implications to call center outsourcing. Oper. Res. 60(4):996-1009.Link, Google Scholar · Zbl 1260.90047 |
| [18] | Gurvich I, Whitt W (2009) Queue-and-idleness-ratio controls in many-server service systems. Math. Oper. Res. 34(2):363-396.Link, Google Scholar · Zbl 1213.60149 |
| [19] | Halfin S, Whitt W (1981) Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3):567-588.Link, Google Scholar · Zbl 0455.60079 |
| [20] | Hossain E, Niyato D, Han Z (2009) Dynamic Spectrum Access and Management in Cognitive Radio Networks (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar · doi:10.1017/CBO9780511609909 |
| [21] | Huang S, Liu X, Ding Z (2008) Opportunistic spectrum access in cognitive radio networks. Proc. 27th Conf. Comp. Comm. (IEEE INFOCOM 2008) (IEEE, Piscataway, NJ), 2101-2109.Google Scholar |
| [22] | Hunt PJ, Kurtz TG (1994) Large loss networks. Stochastic Processes Their Appl. 53(2):363-378.Crossref, Google Scholar · Zbl 0810.60087 · doi:10.1016/0304-4149(94)90071-X |
| [23] | Jaiswal NK (1968) Priority Queues, Mathematics in Science and Engineering (Elsevier Science, New York).Google Scholar · Zbl 0179.47904 |
| [24] | Jia J, Zhang Q, Shen X (2008) HC-MAC: A hardware-constrained cognitive mac for efficient spectrum management. IEEE J. Selected Areas Comm. 26(1):106-117.Crossref, Google Scholar · doi:10.1109/JSAC.2008.080110 |
| [25] | Kurtz TG (1992) Averaging for martingale problems and stochastic approximation. Applied Stochastic Analysis, Lecture Notes in Control and Information Sciences, Vol. 177 (Springer, Berlin), 186-209.Crossref, Google Scholar · doi:10.1007/BFb0007058 |
| [26] | Liu KR, Wang B (2010) Cognitive Radio Networking and Security: A Game-Theoretic View (Cambridge University Press, New York).Crossref, Google Scholar · Zbl 1209.90004 · doi:10.1017/CBO9780511778773 |
| [27] | Luo J, Zhang J (2013) Staffing and control of instant messaging contact centers. Oper. Res. 61(2):328-343.Link, Google Scholar · Zbl 1276.60101 |
| [28] | Maglaras C, Zeevi A (2004) Diffusion approximations for a multiclass Markovian service system with “guaranteed” and “best-effort” service levels. Math. Oper. Res. 29(4):786-813.Link, Google Scholar · Zbl 1082.60068 |
| [29] | Maglaras C, Zeevi A (2005) Pricing and design of differentiated services: Approximate analysis and structural insights. Oper. Res. 53(2):242-262.Link, Google Scholar · Zbl 1165.91371 |
| [30] | Mandelbaum A, Massey W, Reiman M, Stolyar A, Rider B (2002) Queue lengths and waiting times for multiserver queues with abandonment and retrials. Telecomm. Systems 21(2-4):149-171.Crossref, Google Scholar · doi:10.1023/A:1020921829517 |
| [31] | Mishra S, Sahai A, Brodersen R (2006) Cooperative sensing among cognitive radios. Proc. IEEE Internat. Conf. Comm., Vol. 4 (IEEE, Piscataway, NJ), 1658-1663.Google Scholar |
| [32] | Mitola J, Maguire JGQ (1999) Cognitive radio: Making software radios more personal. IEEE Personal Comm. 6(4):13-18.Crossref, Google Scholar · doi:10.1109/98.788210 |
| [33] | Pang G, Perry O (2015) A logarithmic safety staffing rule for contact centers with call blending. Management Sci. 61(1):73-91.Link, Google Scholar |
| [34] | Perry O, Whitt W (2011a) A fluid approximation for service systems responding to unexpected overloads. Oper. Res. 59(5):1159-1170.Link, Google Scholar · Zbl 1233.90124 |
| [35] | Perry O, Whitt W (2011b) An ODE for an overloaded X model involving a stochastic averaging principle. Stochastic Systems 1(1):59-108.Link, Google Scholar · Zbl 1291.60191 |
| [36] | Perry O, Whitt W (2013) A fluid limit for an overloaded X model via an averaging principle. Math. Oper. Res. 38(2):294-349.Link, Google Scholar · Zbl 1305.60024 |
| [37] | Prasad R, Dixit S, van Nee R, Ojanpera T, eds. (2010) Globalization of Mobile and Wireless Communications: Today and in 2020, Signals and Communication Technology (Springer, Dordrecht, Netherlands).Crossref, Google Scholar · Zbl 1196.94013 · doi:10.1007/978-90-481-3437-3 |
| [38] | Puhalskii AA, Reiman MI (2000) The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. Appl. Probab. 32(2):564-595.Crossref, Google Scholar · Zbl 0962.60089 · doi:10.1239/aap/1013540179 |
| [39] | van de Beek J, Riihijarvi J, Achtzehn A, Mahonen P (2012) TV white space in Europe. IEEE Trans. Mobile Comput. 11(2):178-188.Crossref, Google Scholar · doi:10.1109/TMC.2011.203 |
| [40] | Wang J, Baron O, Scheller-Wolf A (2015) M/M/c queue with two priority classes. Oper. Res. 63(3):733-749.Link, Google Scholar · Zbl 1327.90055 |
| [41] | White H, Christie LS (1958) Queuing with preemptive priorities or with breakdown. Oper. Res. 6(1):79-95.Link, Google Scholar · Zbl 1414.90126 |
| [42] | Whitt W (2002) Stochastic-Process Limits. Springer Series in Operations Research (Springer-Verlag, New York).Crossref, Google Scholar · Zbl 0993.60001 · doi:10.1007/b97479 |
| [43] | Whitt W (2006) Fluid models for multiserver queues with abandonments. Oper. Res. 54(1):37-54.Link, Google Scholar · Zbl 1167.90462 |
| [44] | Yang T, Templeton J (1987) A survey on retrial queues. Queueing Syst. 2(3):201-233.Crossref, Google Scholar · Zbl 0658.60124 · doi:10.1007/BF01158899 |
| [45] | Yom-Tov G, Mandelbaum A (2014) Erlang-R: A time-varying queue with reentrant customers, in support of healthcare staffing. Manufacturing Service Oper. Management 16(2):283-299.Link, Google Scholar |
| [46] | Zhan D, Ward AR (2014) Threshold routing to trade off waiting and call resolution in call centers. Manufacturing Service Oper. Management 16(2):220-237.Link, Google Scholar |
| [47] | Zhang Q, Jia J, Zhang J (2009) Cooperative relay to improve diversity in cognitive radio networks. IEEE Comm. Magazine 47(2): 111-117.Crossref, Google Scholar · doi:10.1109/MCOM.2009.4785388 |
| [48] | Zhao Q, · Zbl 1390.94510 · doi:10.1109/TSP.2007.907867 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
