A PRODUCTION INVENTORY MODEL WITH PROTECTION
FOR FEW STAGES OF PRODUCTION
Nisha Mathew, V.C Joshua, A Krishnamoorthy, Ambily
P. Mathew
We consider a two
server production inventory model with positive
service time. Customers arrive to the system
according to a Markovian Arrival Process.
Service time of customers follow identical but
independent phase type
distribution. The
production of inventory follows (s, S) policy.
Production of inventory is by one unit at a time
and the production
time follows Erlang distribution. While in
production shocks occur and consequently
breakdown of the
production machinery takes place.
The shock/damage process occurs according
to a Poisson process. After repair, the
production process restarts, discarding
the item in production. The repair time follows
phase type distribution. In order
to minimize the product loss due to shock,
protection is given to the last k stages of
production. Protection of the
production process involves additional
cost. As a result of this protection, the item,
while in the last k stages of
production, will not be affected by
shocks. Steady state analysis of the model is
performed. Some performance measures
and distributions of certain important
performance characteristics are evaluated. We
formulate an optimization
problem related to the number of stages
of the production process to be protected.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-7-29
SPREADING OF A LIMITED LIFETIME INFORMATION IN
NETWORKS EVOLVING BY PREFERENTIAL ATTACHMENT
Natalia Markovich
The paper is
devoted to the information spreading (propagation)
on random graphs evolving by a linear
preferential attachment (PA) model. The PA is
proposed to play a double role, namely, as the
evolution model, i.e. the tool to add
new edges and nodes to the network and (or)
to remove existing nodes and edges, and as the
spreading tool. We assume that a single message
is to be propagated within a fixed time interval.
In practice, a message may become old and not
relevant. A node having a message
instantaneously passes on information to one of
its neighbour nodes which does not have the
message yet. This neighbour may be either a node
newly appended to the graph or an existing node.
By probabilities of
α−, β− and γ−schemes of the used PA model a new
directed edge is drawn between a new node
appended to the graph and an existing node or a
new edge is drawn between a pair of existing
nodes. By convention the
propagation is provided if the new node (or
one of the existing nodes) without the message
has an incoming edge to an existing node having
the information. Distributions of the number of
nodes that received the message and the total
number of nodes as well as the ratio of
the latter random numbers in a fixed time
interval with regard to parameters of the PA are
obtained.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-30-39
INFINITE-SERVER
QUEUEING SYSTEM WITH WAITING NEGATIVE CUSTOMERS
Danil Korolev,
Svetlana Moiseeva, Alexander Moiseev, Sardor Saidov
The paper
considers a queueing system with waiting
negative customers. The system has two arrival
processes: one for positive customers, another
for negative ones. In this model, arrived
negative customers do not contact with present
positive ones but immediately destroy new
positive arrivals. To find the joint probability
distribution of the number of positive and
negative customers, we use the method of
asymptotic analysis under the condition of high
rate of arrivals. As
the result, we derive the approximation of
characteristic function of the distribution.
Using it, we obtain that onedimensional
stationary probability of the number of positive
customers can be approximated by Gaussian
distribution. Using
numerical evaluations and simulation experiments,
we estimate an error and an applicability area
of the approximation.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-40-50
PARTIAL ASYMPTOTIC ANALYSIS METHOD FOR TWO-CLASS
RETRIAL QUEUE WITH CONSTANT RETRIAL RATE
Ekaterina Fedorova, Anatoly Nazarov, Elena Bulgakova
In the paper, a
single-server retrial queueing system with two
types of arrivals and a constant retrial policy
is considered as a mathematical model of a
multimodal telecommunication network. Service,
inter-arrival and inter-retrial times have
exponential distributions. The constant retrial
policy means that only the first customer from
an orbit performs an attempt to get a service.
The method of partial asymptotic analysis under
a condition of a heavy load of one class of
customers is proposed. The formula for the
asymptotic characteristic function of the
stationary marginal probability distribution of
the number of customers of one class is derived.
In addition, the system stability conditions are
discussed. Some numerical examples are presented.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-51-60
PERFORMANCE AND NUMERICAL ANALYSIS OF (GI GI N, M)
QUEUES USING MARKED MARKOV
PROCESS
Vladimir Rykov,
Nika Ivanova, Evsey Morozov
We study the key
performance characteristics of a finite-buffer
multi-server queuing system denoted as (GI GI n,
m), with general inter-arrival and service times
distributions. The concept called Marked Markov
Processes is employed to
analyze such a system. Its mathematical
model is constructed, and marks’ transformations
are introduced, which are further applied to
calculate the performance characteristics of the
system using a special simulation algorithm.
Numerical study validates the proposed method
employing the comparison of the obtained results
with well-known results for (M|M|1), (M|GI|1),
and (M|M|n, m) models.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-61-82
ON PARTIAL STABILITY OF PREEMPTIVE PRIORITY RETRIAL
MODEL
Ruslana Nekrasova
We consider a
retrial model under constant retrial rate policy
with two classes of customers characterized by
different priorities.
Preemptive priority arrivals, who meet the
server busy by the other class customer,
immediately start the
processing, while interrupted customers lose the
residual service times and join the end of the
corresponding orbit
queue. The system is fed by a superposition of
two Poisson inputs, retrial times are
exponential, service times are
generally distributed and independent and
iid in each class. We study the model in a
partial stable state, when one orbit
queue (independently of its class
priority) is stochastically bounded, and other
orbit infinitely grows in probability. We
rely in preliminary results for a
convenient two-class retrial model with no
interruptions, where partial stability is
equivalent to the transience of an
associated Markov Chain (MC). Based on MC
approach, we obtain transience
conditions for embedded two-dimensional
orbit size process and then verify partial
stability behavior in transient zones
by simulation.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-83-96
ON THE RELIABILITY ESTIMATION OF THE GAUSSIAN
DEGRADATION SYSTEM WITH A
PATH-DEPENDENT MEAN DEGRADATION RATE
Oleg Lukashenko
We consider a
system whose degradation dynamic is described by
an underlying stochastic process that consists
of two components: a
centered Gaussian process and a drift term with
a so-called path-dependent intensity rate, which
means its dependence
on the degradation history. The main goal is to
estimate the reliability of the system via
simulation methods, as
its analytical expression is generally not
available. The cross-entropy method has been
applied to estimate
the required quantity with acceptable accuracy.
A few numerical experiments have been conducted
to study the
properties of the proposed estimator.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-97-107
REGENERATION AND APPROXIMATION OF A QUEUEING SYSTEM
FED BY SUPERPOSED INPUT
WITH WEIBULL COMPONENTS
Irina Peshkova, Michele Pagano, Evsey Morozov
We study a
single-server queueing system with a superposed
input process formed by independent stationary
renewal processes with
Weibull interarrival time distributions. An
approximating system with renewal input process
based on Palm
construction is considered. Moreover, the
accuracy of the approximation in the terms of
Kolmogorov distance is
discussed. Finally, we demonstrate how to
construct, in the initially non-regenerative
queueing system, the artificial
regenerations based on the exponential
splitting technique.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-108-117
QUEUEING-INVENTORY K-OUT-OF-N SYSTEM WITH HEAVY
TAILS
Arya P S, Manikandan Rangaswamy, Alexander
Rumyantsev
In this paper, we
study the so-called k-out-of-n
queueing-inventory system with a single repair
unit, identical elements
that are subject to failure, stock of
spare elements, and state-dependent
replenishment policy. The finite state space
Markov chain model is described, and key
stationary performance measures are defined. The
key focus of this research
is on the non-Markov case, in which the
random repair and replenishment times may have
infinite means, which may
affect the positive recurrence of the
states of the model. This case is investigated
numerically.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-118-129
EXACT SAMPLING FOR HETEROGENEOUS MULTISERVER JOB
MODEL
Alexander S. Golovin
The paper presents
an approach to the simulation of a multi-server
queueing system, known as the multi- server job
model, where the (random number of)
servers are seized/released by a customer
simultaneously. This model is widely
used in scenarios like cloud computing
and parallel processing. Due to the inherent
difficulty in obtaining analytical
solutions for such systems, we adopt the
exact sampling technique to generate the
steady-state workload samples
accurately. This technique allows one to
obtain unbiased estimates of the steady-state
performance, such as the perclass
waiting times of customers.
DOI:
https://doi.org/10.24412/1932-2321-2025-885-130-143
