The possibilities of increasing the probability of timely service and reducing the average waiting time for requests for machine-to-machine exchange in distributed computer systems are investigated. Improving the reliability, timeliness and error-free transmission in automated distributed control systems focused on intelligent and cognitive methods of data and image analysis is fundamental in their real-time operation. The effect is achieved as a result of the reserved multipath transfers of packets critical to delays, at which their replication is provided with a task for each replica of the path (route) of sequential passage of network nodes. An analytical model is proposed for estimating the probability of timely delivery and the average total waiting time in the queues of route nodes with reserved and non-reserved packet transmission. The communication nodes that make up the data transmission route are represented by single-channel queuing systems with an infinite queue. The influence of the multiplicity of redundancy (replication) of transmissions on the probability of their timely maintenance is analyzed. The condition for the success of reserved transfers is that the accumulated total waiting in the queues of nodes that make up the path for at least one of the replicas of the packet should not exceed the given maximum allowed time. The efficiency of destroying expired packets in the intermediate nodes that make up the data transmission paths is shown. The existence of an optimal redundancy multiplicity critical to the total delay in the queues of packets is shown. Fault tolerance, duplicate computer, reliability, redundancy, real time, probability of timely.
The intellectualization of real-time application solutions in automated distributed control systems
requires the support of high reliability and fault tolerance [
A special feature of real-time image transmission and processing is the limitation of acceptable
network delays and transmission delay spread (jitter), which significantly reduce the stability of
communication and the quality of image perception, including video streams. Various methods are used
to deal with transmission errors, the main ones being noise-tolerant coding (including transport coding)
and retransmissions. Retransmissions lead to increased delays, which makes it advisable to use
realtime protocols without delivery confirmations. Solutions to these problems are particularly important
for real-time cyber-physical systems [
2021 Copyright for this paper by its authors.
Transport coding [
The Real-Time Transport Protocol (RTP) and the Resource Reservation Protocol (RSVP) jointly
used with it are aimed at ensuring the timeliness of transfers without delivery confirmations and
retransmissions. RSVP allows you to reserve network resources to implement the required quality of
real-time transmissions over the RTP protocol [
For distributed real-time systems, including image transmission, transmission efficiency is characterized by the average delivery time and the variance of this time. For real-time transmissions, the key quality indicator is the probability of error-free delivery within the maximum allowed time.
The reliability and timeliness of request execution in structurally redundant infocommunication
systems can be improved as a result of redundant servicing of packet transfer requests. In the case of
redundant service, in the case of a request for the transmission of a packet, its copies (replicas) are
formed, delivered to the addressee along different routes (paths). A request to transmit a packet is
considered successful if at least one of the generated replicas is delivered to the addressee in a timely
and error-free manner. When multiple replicas are delivered, all but one is destroyed and not issued to
the addressable subscriber [
Multi-path redundant service, provides for the replication of requests with the assignment for each
of them of the path (route) of the sequential passage of nodes, networks [
The condition for the success of reserved transfers is that the accumulated total waiting in the queues
of nodes that make up the path, for at least one of the copies, should not exceed the specified maximum
allowed time [
The organization and models for estimating the probability of timely error-free delivery of packets to the addressee with multipath transmission redundancy during the passage of replicas of transmitted packets of the sequence of switching nodes that make up the path are proposed in [17,18].
Software models [
The destruction of out-of-date replicas, implemented in intermediate switching links along the replica delivery path, can potentially increase the efficiency of multipath canned transmissions. This article is devoted to the study of this possibility.
The purpose of the article is to study the possibilities of increasing the reliability of timely delivery of packets to the addressee as a result of the elimination of irrelevant packets in the intermediate communication nodes that make up the packet delivery paths.
The study of the effectiveness of the destruction of expired replicas includes the construction of models and estimates of the probability of timely delivery of packets to the addressee through the sequence of communication nodes that make up the path, for cases with and without replication of transmitted packets with and without destruction of expired packets.
Let's consider a system that provides for the formation of a single path for the sequential passage of the communication nodes of the network when requesting a packet to be sent. In this section, we will assume that no transfer reservations are made.
The communication nodes that make up the data transmission route are represented by singlechannel mass service systems with an infinite queue of the M/M/1 type [19, 20].
For the transmission option without destroying expired packets, the intensity of sequential requests to all nodes that make up the path will not change. In this case, expired packets will create an unproductive load on the nodes of the path.
When a packet of nodes composing a path passes sequentially, its waiting time accumulates in the outlines of the passed nodes. As a result, the margin of acceptable waiting time t0 is reduced on average by the total average waiting time in the queues of passed nodes.
If there are n possible non-overlapping routes in the network, then with a uniform distribution of the flow of intensity s requests between routes, the intensity of requests sent along each route will be s n .
The probability of not exceeding the allowed waiting time of the packet when passing the i-th node, taking into account the delays in the queues of the nodes involved in the transmission, is defined as Pi 1 viev1i t0 ai ij11 wj ,
1, if i 1, ai
0, if i 1, wj v 2
j .
1 v j where vi is the average time of packet transmission through the i-th node of the path without taking into account waiting in its queue, Λ is the intensity of the input stream of requests for packet transmission, and wj is the average time of packet waiting in the queue of the j-th node
The probability of timely delivery when passing all m nodes that make up the path is defined as m (4) P Pi ,
i1 where Pi is the conditional probability that the delay in the queue at the i-th node, taking into account the accumulation of waiting at the previous nodes, will not exceed the total allowable delay in the queues t0.
When expired packets are destroyed in intermediate nodes, the intensity of requests to the nodes will decrease as they continue along the route. Destroying expired packets reduces the unproductive load of nodes that make up the packet delivery path to the destination.
The probability of not exceeding the allowed waiting time of the packet during the passage of the ith node, taking into account the reduction in the load of nodes on the meta of the packet promotion and the margin of the allowed total waiting time t0, is defined as
i1 (5)
Pi 1 iviei v1i t0 ai j1 wj , where ai is calculated by (2).
For i=1, 1 and for i>1
i1 (6) i Pi ,
j1 wj jv j2 . (7) 1 v
j j
The probability of timely delivery when passing all m nodes that make up the path is determined by (4) when calculating Pi by (5).
As an additional indicator of the effectiveness of the systems under study, the average delay W in queues when passing m nodes that make up the route can be used. In the case when the destruction of expired packets in intermediate nodes does not occur
m v j2 W .
j1 1 v j If the expired packets in the intermediate nodes are destroyed, then (1) (2) (3) expressing the mathematical expectation of the margin until the maximum allowable delay t0 is reached, the average time of total waiting in the queues of nodes that make up the route for randomly delivered packets.
When calculating, we will assume that the path passes through m=3 nodes, the average transmission time through which (without taking into account waiting in queues), v1= v2= v3=0.1 s, and the maximum allowable total waiting time in the queues of all nodes that make up the path is t0 =0.8 s.
Figure 1 shows the dependence of the probability of timely service of requests for the delivery of packets to the destination, and Figure 2 shows the average waiting time for transmitted packets in the queues of the nodes of the path on the intensity of the input stream of requests Λ. In Fig.1, curves 1-3 correspond to the passage of the path with the destruction of expired packages, and curves 4-6 without their destruction at t0=0.8, 1, 1.5 s. In Fig.2, curves 1 correspond to the total average delay in points when passing the path without destroying expired packets, and curves 2-4 with their destruction at t0=0.8, 1, 1.5 s.
Figure 3 shows the dependence of the complex efficiency indicator Z on the intensity of the input stream of requests Λ. Curves 1-3 correspond to the passage of the path with the destruction of expired packages, and curves 4-6 without their destruction at t0=0.8, 1, 1.5 s.
When reserving transfers (with the creation of k replicas of each transmitted packet), we assume that all paths include m nodes. At the i-th stage (section) of the path, one of the ni nodes with identical characteristics can be used in its formation, the load of which is assumed to be the same. Thus, the probability of timely delivery of a single replica of a packet when passing through all m nodes that make up one of the paths, while not destroying expired replicas of packets in intermediate nodes is calculated as where
P m 1 skvi e nsik v1i t0 ai ij11 wj , i1 ni wj
sk nj v j2 1 sk nj v j , the probability of timely delivery of a single replica of a packet when passing through all m nodes that make up one of the paths, when destroying expired replicas of packets in intermediate nodes, is calculated by (4) when finding Pi according to the formula (5) with substitution for i=1, and for i>1 k i1 (8) i s Pi .
ni j1 In the formula (5) wj is calculated by the formula (7) in the calculation according to the formula (8).
The probability of not exceeding the allowable time t0 of walking all nodes in the path, at least one of the k replicas of the packages, provided that the number of nodes that make up all the way is equal to m, and their characteristics are the same, calculate as
R 1 (1 P)k .
The dependence of the probability of timely reserved service on the intensity of the input stream of requests is shown in Figure 4. Curves 1-3 correspond to the option with the destruction of expired replicas in intermediate nodes, and curves 4-6 correspond to the option without their destruction, respectively, with a redundancy multiplicity of 1, 2, 3. The calculation is performed at t0=0.3 s. The dependence of the probability of timely reserved service on the multiplicity of reserved requests is shown in Figure 5. Curves 1-3 correspond to the variant with the destruction of expired replicas in intermediate nodes, and curves 4-6 correspond to the variant without their destruction, respectively, at t0=0.8, 1, 1.4 s. The calculation is performed at Λ=6 1/s.
The presented graphs confirm the high efficiency of destroying expired packets in intermediate nodes and the existence of an optimal multiplicity of packet redundancy critical to the total delay in the queues of the transmitting nodes. With a decrease in the system load, the recommended redundancy rate for waiting-critical packets, at which the maximum probability of timely delivery of at least one of the replicas of packets is achieved, increases.
Figure 4 shows the feasibility of adaptive changes in the multiplicity of reservation requests as the intensity of the input stream increases. So, for the example under consideration, when the request intensity is low, the transmitted packets should be reserved with a multiplicity of three, as it increases, with a multiplicity of two, and finally, there is a limit on the request intensity above which it is not advisable to reserve packets.
Figure 5 shows the existence of an optimal redundancy multiplicity for requests critical to the total delay in the queues. Moreover, when the expired requests are destroyed, the effect of reserving transfers increases.
The proposed models and technical solutions for ensuring the reliability and timeliness of multipath transmission of packets critical to queue delays are supposed to be adapted for use within the framework of the concept of Ultrareliable and Low-Latency Wireless Communication [21-23].
For requests critical to delays in queues, the influence of the multiplicity of reservation (replication) requests on the probability of their timely service is analyzed.
It is shown that there is an optimal multiplicity of reserving requests critical to the total delay in queues, taking into account options with and without destroying expired packets in the intermediate nodes that make up the paths.
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