Two channel assignment policies are considered for a Kelly type loss network with an additional channel continuity requirement. It is assumed that the channels on any given link have distinct identities, and that a connection should be assigned channels with a common identity on all links of its route. Such constraints arise in circuit switched WDM optical networks and wireless cellular networks. A functional law of large numbers, which was previously developed by Hunt and Kurtz and later refined by Zachary and Ziedins, is adapted to analyze a network with two links and three connection types. Asymptotically exact fluid-type approximations for the network process are obtained and their operating points are characterized. The results lead to asymptotic call blocking rates and point out that in cases of practical interest, random channel assignment has asymptotically the same blocking performance with more sophisticated channel assignment policies.
"Asymptotically exact analysis of a loss network with channel continuity." Ann. Appl. Probab. 13 (4) 1474 - 1493, November 2003. https://doi.org/10.1214/aoap/1069786506