Open AccessThe article presents an analytical model to estimate the mathematical expectation of the data center (DC) response time to the interactive requests from remote users connected to the DC via leased lines (LL), which run under control of HDLC-type protocols for configurations "pointpoint» and "point - multipoint » in Normal Response Mode, NRM. In the logic connection DC acts as the host (primary node) and remote stations play the role of the slave units (secondary nodes).
The objective of research is to obtain analytical expressions to define the following:
- Mathematical expectation of waiting time required for input and output messages of each class to start transmitting via leased line;
- Mathematical expectation of total DC response time to requests of each class.
The process of interaction between remote workstations and DC is formalized as a closed three-node queuing network (QN), wherein the first multi-channel node corresponds to the phase of request deliberation (preparation) to DC on the workstation. In this phase, the number of facilities, i.e. service channels, is equal to the number of workstations (terminals), R. The second single-channel node of this QN reflects processing of input and output messages to the LL in accordance with the logic of HDLC protocol. The third multi-channel node of this NQ reflects, as a matter of fact, processing query to DC. In this node one process in DC corresponds to each active terminal, i.e., the number of facilities is equal to the number of workstations R.
It is shown that the problem of determining the DC average response time to requests of remote users is reduced to the problem of determining the average waiting time for the input and output messages to start transmitting messages by LL - that sort of unknown average waiting time turns out to be 2R. The first two points of the probability distribution functions of reflection time, LL transmission time, and time of message processing, as a matter of fact, in DC are assumed to be specified.
To create a system of algebraic equations in regard to the unknown average waiting time for the input and output messages to start LL sending a so-called method of "labeled transaction" is used. The system of equations is constructed, initially, to provide the "point-multipoint configuration." Then it is shown how to obtain a system for configuration "point-point" as a special case.
The first phase considers an arrival of the "labelled transaction" submitting output message in QN and builds R equations in regard to the unknown average waiting time for the output message to start its sending by LL from DC to the workstation.
The second phase considers an arrival of the "labelled transaction" submitting input message in QN and builds R equations in regard to the unknown average waiting time for the input message to start its sending by LL from the workstation to DC.
The result is a system of the 2R algebraic equations in regard to 2R unknown average waiting time for a start of message transmission by LL. The existence of a unique solution of the resulting system of equations is proved, and a computationally efficient procedure for determining solution as a modified Newton-Kantorovich method is proposed.
The paper shows how to obtain a system of equations for the "point-point" configuration, as a special case, from the system of equations for the "point-multipoint" configuration. It presents the formulas for calculating the DC average response time to remote users’ requests for each workstation.