Abstract
In this paper, we introduce a combinatorial algorithm for the message scheduling problem on Time Division Multiple Access (TDMA) networks. In TDMA networks, time is divided in to slots in which messages are scheduled. The frame length is defined as the total number of slots required for all stations to broadcast without message collisions. The objective is to provide a broadcast schedule of minimum frame length which also provides the maximum throughput. This problem is known to be \(\mathcal{NP}\) -hard, thus efficient heuristics are needed to provide solutions to real-world instances. We present a two-phase algorithm which exploits the combinatorial structure of the problem in order to provide high quality solutions. The first phase finds a feasible frame length in which the throughput is maximized in phase two. Computational results are provided and compared with other heuristics in the literature as well as to the optimal solutions found using a commercial integer programming solver. Experiments on 63 benchmark instances show that the proposed method is able to provide optimal frame lengths for all cases with near optimal throughput.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akyildiz, I.F., Wang, X., Wang, W.: Wireless mesh networks: a survey. Comput. Netw. 47(4), 445–487 (2005)
Balas, E., Landweer, P.R.: Traffic assignment in communications satellites. Oper. Res. Lett. 2, 141–147 (1983)
Bongiovanni, G., Tang, D.T., Wong, C.K.: A general multibeam satellite switching algorithm. IEEE Trans. Commun. 29, 1025–1036 (1981)
Burkard, R.E.: Time-slot assignment for TDMA-systems. Computing 35, 99–112 (1985)
Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86, 165–177 (1990)
Commander, C.W., Butenko, S.I., Pardalos, P.M.: On the performance of heuristics for broadcast scheduling. In: Grundel, D., Murphey, R., Pardalos, P. (eds.) Theory and Algorithms for Cooperative Systems, pp. 63–80. World Scientific, Singapore (2004)
Commander, C.W., Butenko, S.I., Pardalos, P.M., Oliveira, C.A.S.: Reactive grasp with path relinking for the broadcast scheduling problem. In: Proceedings of the 40th Annual International Telemetry Conference, pp. 792–800, 2004
Ephremides, A., Truong, T.V.: Scheduling broadcasts in multihop radio networks. IEEE Trans. Commun. 38(4), 456–460 (1990)
Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)
Festa, P., Resende, M.G.C.: GRASP: An annotated bibliography. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 325–367. Kluwer Academic, Dordrecht (2002)
Ganz, A., Gao, Y.: Efficient algorithms for SS/TDMA scheduling. IEEE Trans. Commun. 40, 1367–1374 (1992)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gomes, F.C., Pardalos, P.M., Oliveira, C.A.S., Resende, M.G.C.: Reactive GRASP with path relinking for channel assignment in mobile phone networks. In: Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 60–67. ACM Press, New York (2001)
Hajek, B., Sasaki, G.: Link scheduling in polynomial time. IEEE Trans. Inform. Theory 34, 910–918 (1988)
Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research. McGraw–Hill, New York (2001)
Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Nonconvex Optimization and its Applications, vol. 3. Kluwer Academic, Dordrecht (1995)
Dash Optimization Inc. Xpress-Optimizer Reference Manual (2003)
Kleinrock, L., Silvester, J.: Spatial reuse in multihop packet radio networks. In: Proceedings of the IEEE 75, 1987
Krivelevich, M.: Sparse graphs usually have exponentially many optimal colorings. Electron. J. Comb. 9, 8 (2002)
Laguna, M., Martí, R.: A GRASP for coloring sparse graphs. Comput. Optim. Appl. 19(2), 165–178 (2001)
Oliveira, C.A.S., Pardalos, P.M., Querido, T.M.: A combinatorial algorithm for message scheduling on controller area networks. Int. J. Oper. Res. 1(1/2), 160–171 (2005)
Pitsoulis, L.S., Resende, M.G.C.: Greedy randomized adaptive search procedures. In: Resende, M.G.C., Pardalos, P.M. (eds.) Handbook of Applied Optimization, pp. 168–183. Oxford University Press, London (2002)
Prais, M., Ribeiro, C.C.: Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J. Comput. 12(3), 164–176 (2000)
Rendl, F.: Personal communication (1986)
Resende, M.G.C., Pardalos, P.M.: Handbook of Optimization in Telecommunications. Springer, Berlin (2006)
Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 219–249. Kluwer Academic, Dordrecht (2003)
Salcedo-Sanz, S., Busoño-Calzón, C., Figueiral-Vidal, A.R.: A mixed neural-genetic algorithm for the broadcast scheduling problem. IEEE Trans. Wirel. Commun. 2(2), 277–283 (2003)
Wang, G., Ansari, N.: Optimal broadcast scheduling in packet radio networks using mean field annealing. IEEE J. Sel. Areas Commun. 15(2), 250–260 (1997)
Wolsey, L.: Integer Programming. Wiley, New York (1998)
Yeo, J., Lee, H., Kim, S.: An efficient broadcast scheduling algorithm for TDMA ad-hoc networks. Comput. Oper. Res. 29, 1793–1806 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Commander, C.W., Pardalos, P.M. A combinatorial algorithm for the TDMA message scheduling problem. Comput Optim Appl 43, 449–463 (2009). https://doi.org/10.1007/s10589-007-9143-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10589-007-9143-8