TY - GEN

T1 - Shortest Path and Maximum Flow Problems under Service Function Chaining Constraints

AU - Sallam, Gamal

AU - Gupta, Gagan R.

AU - Li, Bin

AU - Ji, Bo

N1 - Funding Information:
This work was supported in part by the NSF under Grants CNS-1651947 and CNS-1717108.
Publisher Copyright:
© 2018 IEEE.

PY - 2018/10/8

Y1 - 2018/10/8

N2 - With the advent of Network Function Virtualization (NFV), Physical Network Functions (PNFs) are gradually being replaced by Virtual Network Functions (VNFs) that are hosted on general purpose servers. Depending on the call flows for specific services, the packets need to pass through an ordered set of network functions (physical or virtual) called Service Function Chains (SFC) before reaching the destination. Conceivably for the next few years during this transition, these networks would have a mix of PNFs and VNFs, which brings an interesting mix of network problems that are studied in this paper: (1) How to find an SFC-constrained shortest path between any pair of nodes? (2) What is the achievable SFC-constrained maximum flow? (3) How to place the VNFs such that the cost (the number of nodes to be virtualized) is minimized, while the maximum flow of the original network can still be achieved even under the SFC constraint? In this work, we will try to address such emerging questions. First, for the SFC-constrained shortest path problem, we propose a transformation of the network graph to minimize the computational complexity of subsequent applications of any shortest path algorithm. Second, we formulate the SFC-constrained maximum flow problem as a fractional multicommodity flow problem, and develop a combinatorial algorithm for a special case of practical interest. Third, we prove that the VNFs placement problem is NP-hard and present an alternative Integer Linear Programming (ILP) formulation. Finally, we conduct simulations to elucidate our theoretical results.

AB - With the advent of Network Function Virtualization (NFV), Physical Network Functions (PNFs) are gradually being replaced by Virtual Network Functions (VNFs) that are hosted on general purpose servers. Depending on the call flows for specific services, the packets need to pass through an ordered set of network functions (physical or virtual) called Service Function Chains (SFC) before reaching the destination. Conceivably for the next few years during this transition, these networks would have a mix of PNFs and VNFs, which brings an interesting mix of network problems that are studied in this paper: (1) How to find an SFC-constrained shortest path between any pair of nodes? (2) What is the achievable SFC-constrained maximum flow? (3) How to place the VNFs such that the cost (the number of nodes to be virtualized) is minimized, while the maximum flow of the original network can still be achieved even under the SFC constraint? In this work, we will try to address such emerging questions. First, for the SFC-constrained shortest path problem, we propose a transformation of the network graph to minimize the computational complexity of subsequent applications of any shortest path algorithm. Second, we formulate the SFC-constrained maximum flow problem as a fractional multicommodity flow problem, and develop a combinatorial algorithm for a special case of practical interest. Third, we prove that the VNFs placement problem is NP-hard and present an alternative Integer Linear Programming (ILP) formulation. Finally, we conduct simulations to elucidate our theoretical results.

UR - http://www.scopus.com/inward/record.url?scp=85056169812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056169812&partnerID=8YFLogxK

U2 - 10.1109/INFOCOM.2018.8485996

DO - 10.1109/INFOCOM.2018.8485996

M3 - Conference contribution

AN - SCOPUS:85056169812

T3 - Proceedings - IEEE INFOCOM

SP - 2132

EP - 2140

BT - INFOCOM 2018 - IEEE Conference on Computer Communications

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE Conference on Computer Communications, INFOCOM 2018

Y2 - 15 April 2018 through 19 April 2018

ER -