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implies that an MSC that supports CAMEL phase 4 shall support MO-SMS-CSI, SS-CSI, TIFCSI (if the MSC supports call de ection) and M-CSI Likewise, an SGSN that supports CAMEL phase 4 shall support MO-SMS-CSI PSI enhancements relates to the SGSN s capability to receive and process MAP PSI, for the purpose of GPRS ATI Although ATI for CS subscribers is also enhanced in CAMEL phase 4, there is no dedicated CAMEL phase 4 subset to signal that capability from MSC to HLR When the subscriber registers in the MSC or SGSN and the HLR has received the indication of supported CAMEL phases and supported CAMEL phase 4 subsets, the HLR shall take care not to send any non-supported CAMEL phase 4 (variant) CSI to that MSC or SGSN Offered CAMEL 4 Functionalities When a CAMEL relationship is started between the gsmSSF (in VMSC or GMSC) and the gsmSCF, the gsmSSF reports to the gsmSCF the CAMEL phase 4 functionalities supported in that gsmSSF Offered CAMEL 4 functionalities indicates which CAP v4 call control capabilities are supported by the (G)MSC/gsmSSF These capabilities are features that are introduced in CAMEL phase 4 The gsmSSF may report a combination of the CAMEL phase 4 functionalities in Table 63 Each of the functionalities in Table 63 is described below A CAMEL service logic will not use capability that is not explicitly indicated Otherwise, service logic processing may fail The offered CAMEL 4 functionalities indication does not replace other CAMEL dialogue rules For example, when a dialled service is triggered with D-CSI and offered CAMEL 4 functionalities indicates, amongst others, alerting DP , then the CAMEL service is still not entitled to arm the alerting DP The reason is that arming the alerting DP is not permissible for a dialled service1

where is the diagonal matrix =diag( 0 , 1 , , m ) and QT is the transpose of the transition matrix Q = (qst ), s, t = 0, 1, , m with qst = st for t = s and qss = t=s st For the special case of m = 1 with 01 = 1 and 10 = 2 (switched Poisson process), verify that the determination of reduces to nding the smallest root of [( 1 + + 1 )z 1 z (z) ][( 2 + + 2 )z 2 z (z) ] 1 2 z2 = 0 on the interval (1, R) Conclude that the geometric tail approach can be applied to calculate the state probabilities p(i, s) (b) Let j denote the long-run fraction of customers who nd j other customers present upon arrival Argue that j = m s p (j, s) / m s es s=0 s=0 (c) Let Wq (x) denote the limiting probability distribution function of the delay in queue of a customer Verify that 1 Wq (x) e (1 )x as x for some constant

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Queueing problems have laid the foundation for the continuous-time Markov chain model The Erlang delay model and the Erlang loss model stem from teletraf c analysis The square-root rule is discussed in many papers and was obtained by AK Erlang in an unpublished paper in 1924 Recommended references are Borst

et al (2003), Hal n and Whitt (1981), Jennings et al (1996) and Whitt (1992) In uential papers showing Poisson departures for the M/M/c queue are Burke (1956) and Reich (1957) Insensitivity is a fundamental concept in stochastic service systems with no queueing The illustrative problem from Example 542 is adapted from Foschini et al (1981) A general discussion of the insensitivity phenomenon in stochastic networks can be found in Kelly (1979, 1991) and Van Dijk (1993) The book of Kelly (1979) makes extensive use of the concept of time-reversible Markov chains The method of phases using ctitious stages with exponentially distributed lifetimes has its origin in the pioneering work of Erlang on stochastic processes in the early 1900s The scope of this method was considerably enlarged by Schassberger (1973), who showed that the probability distribution of any non-negative random variable can be represented as the limit of a sequence of mixtures of Erlangian distributions with the same scale parameters This result is very useful for both analytical and computational purposes The product-form solution was rst obtained in the paper of RRP Jackson (1954) for a tandem queue consisting of two single-server stations This work was considerably extended by JR Jackson (1957, 1963) to produce what have come to be known as Jackson networks More material on queueing networks and their applications in computer and communication networks can be found in the books of Hayes (1984) and Kleinrock (1976)

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