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We propose a new algorithm called enhanced best effort quality of service routing with multiple metrics (EBQRMM). It is proposed for connection oriented point-to-point communications. It applies the concept of the analytic hierarchy process (AHP) which is a well-known model in the area of decision making with multiple objectives. Four metrics have been considered: delay, bandwidth, security and loss probability. Its performance is compared to the single compounded metric, SCM, algorithm. It is found that EBQRMM outperforms SCM over the utilisation range (0-90)% by an average of 10.6% with 1.2% standard deviation. The main novelty of this paper is the application of the AHP approach which provides an opportunity to consider multiple metrics and path selection in the proposed algorithm.