mathematical model
Study the working characteristics of the wiring harness. The key problem is to solve the state probability distribution of the harness. The basic mathematical model of the wiring harness is the process of addition and elimination, which assumes: ① In a very small Δt time, the wiring harness can only be transferred from the current state to the adjacent state or no state change occurs. For example, the number of calls in a harness can be seen as the state of the harness. If there are n calls, the current state is En. Its adjacent state is En-1 or En plus 1. ②The current state of the harness is En, and the conditional transition probability of transitioning to the state En plus 1 at the same time after △t is λn△t plus 0(△t), where λn is the call intensity in the En state. 0(Δt) represents a higher-order infinitesimal of Δt. ③ The current state of the harness is En, and the conditional transition probability is μnΔt plus 0(t), where μn is the call end strength in the En state.
A series of problems related to the load capacity of the wire harness can be solved on the basis of the probability distribution of the wire harness state given by the addition and cancellation process.
1. Harness Utilization
Refers to the number of service devices that can be used by any load source in the load source group. In a partial utilization harness, it is impossible for any load source to use the full capacity of the harness, but only a part of the equipment. Use K to represent the harness utilization, V to represent the harness capacity, then there is V Greater than or equal to K. When V=K, the harness is at full utilization, and the size of utilization K is restricted by the structure of the wiring device.
2. Harness utilization
Refers to the efficiency of harness usage. It is numerically equal to the average completed traffic intensity per line. Using η to represent the harness utilization, then there is
n
In the formula, A0 and A are the completed traffic intensity and incoming traffic intensity of the wire harness respectively, V is the capacity of the wire harness, and E is the loss probability of the wire harness.
One of the tasks of the telecommunications system designer is to form a network with high utilization rate under the premise of a certain quality of service, that is, to form the most economical wiring harness structure and application method. Harness utilization and wire harness load, capacity, structure and service quality are interrelated and mutually restrictive. Taking the loss-made harness as an example, under a certain call loss condition, the larger the harness capacity, the higher the harness utilization rate. For a certain capacity harness, the larger the call loss, the higher the harness utilization rate.
3. Overload of wiring harness
Refers to the situation that the wiring harness is running at a larger load than the rated load. In the actual telecommunication system, the wiring harness is sometimes overloaded. Overloading will degrade the service quality of the wiring harness. The correct design should be such that when the overload is within the allowable range, the degradation of the quality of service should be limited to the given range. To meet this requirement, the harness utilization rate cannot be increased without limit. Harnesses with high utilization are very sensitive to overload.
