A Bounded Item Bin Packing Problem over Discrete Distribution

In this paper we formulate a bounded item bin packing problem over discrete distribution (BIBPPOD) in computer and communication networks, and consider the average performance ratio for next fit algorithm. An efficient average-case analysis procedure for finding the average performance ratio and problem solution is demonstrated. We give the closed-form expression for some special range to which the bounded item belongs. Our result is useful for designing the length in fixed-size format or evaluating the performance impacted by the protocol header in computer and communication network.

[1]  Sungsoo Park,et al.  An Integer Programming Approach to the Bandwidth Packing Problem , 1996 .

[2]  Raphael Rom,et al.  Average Case Analysis of Bounded Space Bin Packing Algorithms , 2007, Algorithmica.

[3]  Jennifer Ryan,et al.  A column generation algorithm for bandwidth packing , 1993, Telecommun. Syst..

[4]  Douglas Comer,et al.  Internetworking with TCP/IP , 1988 .

[5]  H. Zimmermann,et al.  OSI Reference Model - The ISO Model of Architecture for Open Systems Interconnection , 1980, IEEE Transactions on Communications.

[6]  Raphael Rom,et al.  Analysis of Transmissions Scheduling with Packet Fragmentation , 2001, Discret. Math. Theor. Comput. Sci..

[7]  Alexander L. Stolyar,et al.  Bandwidth packing , 2007, Algorithmica.

[8]  Anja Feldmann,et al.  COMPUTING CALL ADMISSION CAPACITIES IN LINEAR NETWORKS , 1999 .

[9]  F. Glover,et al.  Bandwidth packing: a tabu search approach , 1993 .

[10]  Edward G. Coffman,et al.  Probabilistic analysis of packing and partitioning algorithms , 1991, Wiley-Interscience series in discrete mathematics and optimization.

[11]  Christian Hofmann,et al.  Supplier's pricing policy in a Just-in-Time environment , 2000, Comput. Oper. Res..

[12]  Mihalis Yannakakis,et al.  Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packings , 2000, SIAM J. Discret. Math..

[13]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[14]  Edward G. Coffman,et al.  Stochastic analysis of a slotted FIFO communication channel , 1993, IEEE Trans. Inf. Theory.

[15]  Micha Hofri,et al.  A Stochastic Model of Bin-Packing , 1980, Inf. Control..

[16]  N. Karmarkar Probabilistic analysis of some bin-packing problems , 1982, FOCS 1982.

[17]  Wansoo T. Rhee,et al.  Martingale Inequalities and NP-Complete Problems , 1987, Math. Oper. Res..

[18]  Kenneth P. Bogart,et al.  Introductory Combinatorics , 1977 .