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into this powerful method, which is widely used by practitioners The proofs of the results below are deferred to Section 43 The starting point is a continuous-time Markov chain {X(t)} with state space I and in nitesimal transition rates qij for i, j I with j = i As before, let i =

.

qij ,

The quantity i is the parameter of the exponentially distributed sojourn time in state i It is assumed that the i satisfy Assumption 412 For any t 0, de ne the probability pij (t) by pij (t) = P {X(t) = j | X(0) = i}, i, j I

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The computation of the transient probabilities pij (t) will be discussed in Section 45 A deep result from continuous-time Markov chain theory is that limt pij (t) always exists for all i, j I The issue of possible periodicity in the state transitions is not relevant for continuous-time Markov chains, since the times between state transitions have a continuous distribution To ensure that the limits of the pij (t) are independent of the initial state i and constitute a probability distribution, we need the following assumption Assumption 421 The process {X(t), t 0} has a regeneration state r such that P { r < | X(0) = i} = 1 f or all i I and E( r | X(0) = r) < ,

where r is the rst epoch beyond epoch 0 at which the process {X(t)} makes a transition into state r In other words, state r will ultimately be reached with probability 1 from any other state and the mean recurrence time from state r to itself is nite Under this assumption it can be proved that there is a probability distribution {pj , j I } such that

is barred from using an SMSC in another country If the CAMEL service modi es the SMSC address, then BOIC is checked against the modi ed SMSC address Barring of outgoing international calls except to home country the handling for BOIC-exHC is the same as the handling for BOIC BOIC-exHC allows an SMSC to be used in the home country of the subscriber or in the visited country If the CAMEL service modi es the SMSC address, then BOIC-exHC is checked against the modi ed SMSC address CB applies to both SMS-Submit and SMS-Command The other CB categories, BAIC and barring of incoming calls when roaming (BIC-Roam), do not affect on MO-SMS ODB has the same effect as CB ODB may be used to bar the sending of an SMS, either conditionally or unconditionally When SMS submission or SMS command fails as a result of CB or ODB, the CAMEL service is informed by means of the O SMS Failure noti cation 549 Service Examples The present section contains a number of service examples for successful and unsuccessful SMS submissions Figure 568 depicts successful SMS submission without CAMEL-modi ed data The CAMEL service performs a credit check and, upon af rmative response from the charging system, arms the SMS events and allows SMS submission to continue Actual credit deduction takes place when the CAMEL service has received a noti cation that the SMS is successfully submitted to the SMSC The gure also depicts unsuccessful SMS submission In that case, the credit is released in the charging system; the credit that was reserved at the beginning of the service is now available again for other services The use of RT-SMS and the use of FCI-SMS at the start of the service and at SMS submission are optional In Figure 569, the charging system has determined that the SMS may be submitted toll-free The CAMEL service does not keep the CAMEL service active Alternatively, the charging system may need to monitor the SMS submission, in order to keep track of the number of successful toll-free SMSs 5410 International Roaming When CAMEL control of MO-SMS is used in international environment, then the operator needs to cater for the situation that the subscriber registers in a network that does not support CAMEL phase 3 The HLR of the roaming subscriber determines the fallback action that should be taken during registration in the MSC This fallback action is operator-speci c and is not de ned by CAMEL.

lim pij (t) = pj ,

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