Читайте также:
|
Models with multi-class loading of port are applied in networks ISDN and LAN (group receipt, turn of a priority, multidimensional, mixed with losses and with delay, models with multiturns etc.).
In networks with package switching the message breaks into packages which can be approximated as model with group receipt. The model with group receipt assumes that packages of the given message arrive on destination simultaneously.
As the size of group in model is called casual variable Х which is defined on number of the calls simultaneously staying in group. If the group finds all servers occupied at the moment of receipt all calls in group are lost. If the number of free servers is less than the size of group group call acceptance carry out on any one of two strategy: PBAS / WBAS. At studying of a material of a theme it is necessary to acquire the accepted designations and indicators of quality of model, appointment of making elements of the diagramme of conditions of transition. It is necessary to pay attention to the distinctions connected with a kind of distribution (экспоненциальное, geometrical etc.) of arriving streams of not ordinary calls.
At waiting time calculation in model it is necessary to use approximation under Kramer's formula and Langenbaha-Belza and to seize skills of using SCV Ca and Cs.
It is known that the multiserver of lossy systems and the arbitrary holding time M/G/s (0) is equivalent to Markov model M/M/s (0), and the probability of lock here is set by the formula of the Erlang of V.Krome togo, probability of lock for system with restricted number of inputs from n sources M (n)/G/s (0) set by losses under the formula of Engseta. The given properties concern robustness of service time.
It is known that system M/G/1 has stable conditions, if and only if offered transport loading a = r = lh <1 erl where h there is an average holding time, and r - system occupation efficiency. It can be understood intuitively because the server can service 1 erl, as a maximum.
Let's select some call and we mark it as a test call (fig. 10 see). Probability of that the server is occupied, when the test call arrives, on property of 3 loadings and PASTA(Poisson arrivals see time average,т.е это Пуассоновское поступление вызовов, наблюдаемое за среднее время) is equal and. Time until will be completed call service, is residual service time. From here, designating an average residual holding time the character, average of expecting calls - and an average waiting time - we have the following dependence at the order of call service FIFO: formula (18)
On the right side of expression (18) the first product corresponds to average time for a call in service if some has to be completed, and the second product corresponds to service of those expecting calls which stand in a queue ahead of a test call.
Using the formula of Littla = l and solving dependence (18), we receive an average waiting time formula (19)
From expression (16) we receive average residual time (20)
Where Cs2 = σs2/h2 - is SCV service time (service);
σs2 - Is a dispersion of service time (service).
Substituting average residual time (20) in an average waiting time (19), we receive the formula of Poljacheka-Hinchina: formula (21)
In stochastic process time moment in which property of Markov behavior keeps, called as a pulsing point. For system M/G/1 the epoch of deportation (clearing) in which the call is completed and abandons system, becomes a pulsing point.
Markov process with the discrete space of states is called as the Markov circuit. In the Markov circuit all times of epoch in which a state changes, become pulsing points. On the other hand, stochastic process is called as the implemented (nested) Markov circuit if pulsing points are implemented or put during special time of epoch, such as deportation (clearing) of a call in systems of type M/G/1.
In the implemented Markov circuit (fig. 11 see) a state of probability Пj* just after clearing (call deportation) to equally state of probability Пj just before call arrival in stable conditions. From PASTA(Poisson arrivals see time average,т.е это Пуассоновское поступление вызовов, наблюдаемое за среднее время) follows that if in system M/G/1 exists j calls, Pj = Пj = Пj*.
Дата добавления: 2015-02-16; просмотров: 86 | Поможем написать вашу работу | Нарушение авторских прав |