In a series of papers, Generalized Net (GN, see the
Appendix) models of processes, related to tracking the changes
in health status of adult patients have been presented (see, e.g.,
[1, 2]). They are a continuation of the ideas for description of
processes, taking place in hospital units, using the apparatus of
GNs (see, e.g., [3–5]). The so constructed nets give the
possibility to model the logical conditions for the realization of
the processes, to simulate these processes, as well as search
ways for their optimization.
In [1], the processes for generation of signals from sensors
around adult patients and their transmission through different
telecommunication tools to the respective hospital units, have
been described. In [2], a GN-model of the telecommunication
processes between the adult patients and hospital units, has
been discussed. Below, a GN-model of the processes for signal
classification and the reaction of the medical staff of the
hospital units, is constructed. In the Appendix, short remarks of
GNs are given.
The GN model (see Fig. 1) consists of.
• six transitions Z1, Z2, Z3, Z4, Z5 and Z6.
• sixteen places l1, l2, …, l16.
• four different types of tokens representing the patients,
the dispatchers that monitor the signals from the sen-
sors, the medical doctors who examine the patients and
the medical specialists.
The tokens π1, π2, ..., πk which represent the patients enter
the net in place l4 with initial characteristic “patient; name of
the patient; current health status”.
The tokens δ1, δ2, …, δl which represent dispatchers enter
the net in place l8 with initial characteristic: “dispatcher; name
of the dispatcher; information about all received signals”.
The tokens μ1, μ2, ..., μm which represent the medical
doctors who examine the patients enter the net in place l9 with
initial characteristic: “medical doctor; name of the medical
doctor; specialty”.
The tokens σ1, σ2, ..., σm which represent the medical
specialists who examine the patients enter the net in place l9
with initial characteristic: “medical doctor; name of the
medical doctor; specialty”.
The six transitions will be described in details below.
The first transition Z1 has the form:
Z1 = 〈{l4, l10, l15}, {l1, l2, l3, l4}, R1〉,
where
,
15
10
4,43,42,44
4321
1
truefalsefalsefalsel
falsefalsefalsetruel
WWWfalsel
llll
R=
and the predicates in the index matrix R1 have the meanings:
• W4,2 = “the sensor detected a change in patient’s condition”,
• W4,3 = “the patient should be transported to hospital”
• W4,4 = ¬ W4,2 ,
where ¬ P is the negation of the predicate P.
When the truth-value of the predicate W4,2 is true, the token
πi enters place l2 with characteristic “signal of the sensor about
the current patient”.
When the truth-value of the predicate W4,3 is true, the token
πi enters place l3 with characteristic “name of the patient;
current status”.
In place l4, the π-tokens receive the characteristic “current
status of the patient”.
1. Introduction
2. The Generalized Net Model
Generalized Net Model for Telecommunication
Processes in Telecare Services
MIKHAIL MATVEEV, VELIN ANDONOV,
KRASSIMIR ATANASSOV (IEEE Member)
Institute of Biophysics and Biomedical Engineering
Bulgarian Academy of Sciences, Sofia, BULGARIA
MARIA MILANOVA
Multi-profile Hospital for Active Medical Treatment
and Emergency Medicine "N.I.Pirogov"
Sofia, BULGARIA
Abstract: In a series of papers, Generalized Net (GN) models of processes, related to tracking changes in the
health status of adult patients, have been presented. The contemporary state-ofthe- art of the telecommunications
and navigation technologies allow these models to be further extended to the case of active and mobile patients.
This requires the inclusion of patient’s current location as a new and significant variable of the model. Various
opportunities are considered for the retrieval of this information, with a specific focus on the optimal ones, and
a refined GN model is herewith proposed.
Keywords: Generalized nets, Modelling, Telecare, Telecare services.
Received: July 10, 2021. Revised: December 14, 2021. Accepted: December 27, 2021. Published: January 20, 2022.
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Fig. 1. GN model of the telecommunication processes,
taking place in telecare services
The second transition Z2 has the following form:
Z2 = 〈{l2, l8}, {l5, l6, l7, l8}, R2〉,
where
,
8
7,26,25,22
8765
2
truefalsefalsefalsel
falseWWWl
llll
R=
and the predicates in the index matrix R2 have the meanings:
• W2,5 = “medical doctor should be sent to perform examin-
ation of the patient at home”,
• W2,6 = “no action is necessary”,
• W2,7 = “the patient should be transported to a medical center”.
When the truth-value of the predicate W2,5 is true, the token
πi enters place l5 with characteristic “a decision to visit the
patient has been taken”.
When the truth-value of the predicate W2,6 is true, the token
πi enters place l6 with characteristic “a decision to ignore the
signal has been taken”.
When the truth-value of the predicate W2,7 is true, the token
πi enters place l7 with characteristic “a decision to transport the
patient to a medical center has been taken”.
The third transition Z3 has the form:
Z3 = 〈{l1, l5, l9}, {l9, l10}, R3〉,
where
,
10,99,99
5
1
109
3
WWl
falsetruel
falsetruel
ll
R=
and the predicates in the index matrix R3 have the meanings
• W9,10 = “a medical doctor should be sent to examine the
patient”,
• W9,9 = ¬ W9,10.
In place l9, the μ-tokens do not obtain any new charact-
eristics.
When the truth-value of the predicate W9,10 is true, the
corresponding μi token representing the medical doctor enters
place l10 with characteristic “name of the medical doctor who
will visit the patient”.
The forth transition Z4 has the following form:
Z4 = 〈{l7, l12, l13}, {l11, l12}, R4〉,
where
,
13
12,1211,1212
7
1211
4
truefalsel
WWl
truefalsel
ll
R=
and the predicates in the index matrix R4 have the meanings
• W12,11 = “specialists should be sent to bring the patient to
the hospital”;
• W12,12 = ¬ W12,11.
In place l11 the current token σi receives the characteristic
“names of the specialists who will bring the patient to the
hospital”.
In place l12 the tokens receive the characteristic “names of
the staff on duty”.
The fourth transition Z5 has the form:
Z5 = 〈{l3, l11}, {l13, l14}, R5〉,
where
.
11
3
1413
5
falsetruel
truefalsel
ll
R=
In place l13, the tokens receive the characteristic “time for
completing the transportation of the patient”.
In place l14, the tokens receive the characteristic “condition
of the patient upon arrival at the hospital”.
The sixth, final, transition Z6 has the following form:
Z6 = 〈{l14, l16}, {l15, l16}, R6〉,
where
,
16,1615,1616
14
1615
6
WWl
truefalsel
ll
R=
and the predicates in the index matrix R6 have the meanings
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• W16,15 = “all medical procedures are completed”;
• W16,16 = ¬ W16,15.
In place l15, the current πi token receives the characteristic
“condition of the patient upon discharge from hospital”.
In place l16, the current πi token receives the characteristic
“condition of the patient during the procedures”.
Finally, we mention that place l8 represents the processes,
described by the GN from [3], while places l14, l15 and l16
correspond to the processes, modeled by the GN from [4]. On
the other hand, the present GN model elaborates into further
details the basic idea presented in [5].
The so constructed GN model traces the logical stages of the
final part of the process of communication between the sensors
connecting mobile adult patients and the staff of the respective
hospital unit. The developed model can be used for simulation
of the processes of decision making of the appropriate
specialists, who must either visit the respective adult patient or
to transport him/her to the hospital unit. The model permits
simulation of different scenarios e.g. the situation, in which
many patients simultaneously require medical assistance.
This work was partly funded by the project FP7-PEOPLE-
2009-IRSES-247541-MATSIQEL.
[1] Andonov, V., et al. Generalized Net Model for Telecare
Services, IEEE Conf. “Intelligent Systems”, Sofia, Bulgaria, 6-8
Sept. 2012, 221-224.
[2] Andonov, V., T. Stojanov, K. Atanassov, P. Kovachev, General-
ized Net Model for Telecommunication Processes in Telecare
Services, 1st International Conference on Telecommunications and
Remote Sensing, Sofia, Bulgaria, 29-30 Aug. 2012, 158-162.
[3] Chakarov, V., et al. Generalized net model for some basic
clinical administrative decision making. 1st European Conf-
erence on Health Care Modelling and Computation Craiova,
Aug. 31 - Sept., 2, 2005, 72-78.
[4] Matveev M., et al. Dynamic model of intensive care unit work-
flow based on generalized nets. International Electronic Journal
“Bioautomation”, Vol. 2, 2005, 85-92.
[5] Shannon, A., et al. The generalized net modelling of information
healthcare system. Int. Conf. "Automatics and Informatics'06",
Sofia, 3-6 Oct. 2006, 119-122.
[6] Atanassov, K., Generalized Nets, World Scientific, Singapore,
1991.
[7] Atanassov, K., On Generalized Nets Theory, “Prof. Marin Dri-
nov” Publishing House of the Bulgarian Academy of Sciences,
2007.
APPENDIX: SHORT REMARKS ON GENERALIZED NETS
Generalized Nets (GNs, see [6, 7] are extensions of the
apparatus of mathematical modelling of Petri Nets and other
modifications of theirs. GNs are a tool intended for the
detailed modelling of parallel and concurrent processes.
A GN is a collection of transitions and places ordered
according to some rules (see Fig. 2). The places are marked by
circles. The set of places to the left of the vertical line (the
transition) are called input places, and those to the right are
called output places. For each transition, there is an index
matrix with elements called predicates. Some GN-places
contain tokens – dynamic elements entering the net with initial
characteristics and getting new ones while moving within the
net. Tokens proceed from an input to an output place of the
transition if the predicate corresponding to this pair of places
in the index matrix is evaluated as “true”. Every token has its
own identifier and collects its own history that could influence
the development of the whole process modelled by the GNs.
Two time-moments are specified for the GNs: for the
beginning and the end of functioning, respectively.
A GN can have only a part of its components. In this case,
it is called reduced GN. Here, we shall give the formal
definition of a reduced GN without temporal components,
place and arc capacities, and token, place and transition
priorities.
Formally, every transition in the used below reduced GN is
described by a triple: Z = 〈L′, L″, r〉, where:
l'
1
l'
m
Z
l"
1
. . . . . .
l'
i
. . . . . .
l"
n
l"
j
Fig. 2. A GN transition
(a) L′ and L″ are finite, non-empty sets of places (the tran-
sition’s input and output places, respectively); for the
transition these are
L′ = {
m21
'l,...,'l,'l
} and L″ = {
n21
"l,...,"l,"l
};
(b) r is the transition’s condition determining which tokens
will pass (or transfer) from the transition’s inputs to its
outputs; it has the form of an Index Matrix (IM):
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(Attribution 4.0 International, CC BY 4.0)
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Commons Attribution License 4.0
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3. Conclusions
Acknowledgment
References
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)1,1(
)(
'
...
'
...
'"..."..."
,
,
1
1
njmi
predicater
r
l
l
llll
r
ji
ji
m
i
nj
≤≤≤≤
−
=
where ri,j is the predicate that corresponds to the i-th input
and j-th output place. When its truth value is “true”, a
token from the i-th input place transfers to the j-th output
place; otherwise, this is not possible.
The ordered four-tuple
E = 〈A, K, X,
Φ
〉
is called a reduced Generalized Net if:
(a) A is the set of transitions;
(b) K is the set of the GN’s tokens;
(c) X is the set of all initial characteristics which the tokens
can obtain on entering the net;
(d)
Φ
is the characteristic function that assigns new
characteristics to every token when it makes the transfer
from an input to an output place of a given transition.
Many mathematical operations (e.g., union, intersection and
others), relations (e.g., inclusion, coincidence and others) and
operators are defined over the GNs. Operators, being of six
types (global, local, hierarchical, reducing, extending and
dynamic operators) change the structure of the GN, the
strategies of token transfer, etc.
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