Blocking Probabilities for a Single Link with Trunk Reservation

✍ Scribed by J.A. Morrison

• Book ID: 102591283
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 290 KB
• Volume: 203
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0388

✦ Synopsis

A single link in a circuit-switched network is considered. The link has C circuits, Ž . R of which are reserved for the primary directly offered traffic. Offered calls arrive in independent Poisson streams with mean rates and for the primary Ž . and secondary rerouted traffic, respectively, and corresponding independent and exponentially distributed holding times with means 1 and 1r. A primary call requires just 1 circuit, whereas a secondary call requires t circuits, where t is a positive integer. A primary call is blocked on arrival if all C circuits are busy, whereas a secondary call is blocked if more than C y R y t circuits are busy. Blocked calls are lost to the link. The critically loaded case in which c 1, ' ' ' Ž . Ž . Ž . CysO , RsO , and s ␥ , where ␥ s O 1 , is investigated. Asymptotic approximations to B and B , the blocking probabilities for the ' Ž . not if / 1 and R s O . Interestingly, Roberts' approximation corresponds to truncation with just 2 coefficients. Truncation with more coefficients leads to refinements of his approximation.