JIMO

In this paper, we present an enhanced power saving class (PSC)
type III by introducing a sleep-delay mechanism into the
conventional PSC type III in the IEEE 802.16e network. Two
multiple vacation queueing models: without sleep-delay and with
sleep-delay, are built to capture the working principles of the
conventional PSC type III and the enhanced PSC type III,
respectively. Then, using the boundary state variable theory
method, we analyze these queueing models and give the performance
measures in terms of the switch ratio, the power saving ratio, the
average response time and the system utility for both the
conventional and the enhanced power saving schemes. Next,
numerical results are given to demonstrate the dependency
relationships between the performance measures and the sleep
window size. Moreover, we compare the performance of the both
systems without sleep-delay (the conventional PSC type III) and
with sleep-delay (the enhanced PSC type III) to validate the
effect of the sleep-delay mechanism in the enhanced PSC type III
proposed in this paper. Finally, we also construct a cost function
to determine the optimal time length of the sleep-delay timer for
minimizing the cost function.

JIMO

In this paper, we consider an M/M/1 queueing system with impatient
customers and a variant of multiple vacation policy, where we
examine the case that customer impatience is due to the servers'
vacation. Whenever a system becomes empty, the server takes a
vacation. However, the server is allowed to take a maximum number
$K$ of vacations if the system remains empty after the end of a
vacation. This vacation policy includes both a single vacation and
multiple vacations as special cases. We derive the probability
generating functions of the steady-state probabilities and obtain
the closed-form expressions of the system sizes when the server is
in different states. We further make comparisons between the mean
system sizes under the variant vacation policy and the mean system
sizes under the single vacation policy or the multiple vacation
policy. In addition, we obtain the closed-form expressions for other
important performance measures and discuss their monotonicity with
respect $K$. Finally, we present some numerical results to show the
effects of some parameters on some performance measures.

JIMO

With the development of communication technology, the functions of
the mobile terminals are becoming ever more enhanced, and the energy
requirements for the terminals become harder than before. In this
paper we propose a novel Active Discontinuous Reception (DRX)
mechanism with a sleep-delay strategy in the Long Term Evolution
(LTE) technology in order to reduce the average latency while saving
more energy in 4G networks. The key idea is to influence the control
of the downlink transmission on that way that the system would go to
sleep only when there is no data frame arrival within the
sleep-delay timer. Considering several logical channels for one
connection, we model the network using the novel Active DRX
mechanism with a sleep-delay strategy as a multiple synchronous
vacation queueing system with a wake-up period and a sleep-delay. We
derive several performance measures, such as the energy saving
ratio, the system blocking ratio and the average latency. We also
provide numerical results by means of analysis and simulation to
show the validity of the novel Active DRX mechanism. Finally by
constructing a profit function, we optimize several system
parameters in terms of the number of the logical channels for one
connection, the time lengths of the sleep-delay timer and the sleep
period.

JIMO

We discuss the problem of the optimal
liquidation of a financial product in which both the market risk
of the asset and the market impact of the investor's own dealings
are considered, and where the asset is liquidated over several
sales periods with a constant sales interval. The investor chooses
the sales volume in each period as well as the volume over the
entire sales period in order to minimize the expected execution
costs under a certain level of risk. We obtain an explicit
solution for the optimal execution strategies and present four
numerical examples to show that the proportion between market risk
and liquidity risk exerts a major influence over the optimal
execution strategy. We also show that to obtain the optimal result
the investor should liquidate his holdings over a short sales
period.

JIMO

In this paper we consider the analysis of a tandem queueing model
$M/G/1 -> ./M/1$. In contrast to the vast majority of the previous
literature on tandem queuing models we consider the case with GI
service time at the first queue and with infinite buffers. The
system can be described by an M/G/1-type Markov process at the
departure epochs of the first queue. The main result of the paper is
the steady-state vector generating function at the embedded epochs,
which characterizes the joint distribution of the number of
customers at both queues. The steady-state Laplace-Stieljes
transform and the mean of the sojourn time of the customers in the
system are also obtained.

We provide numerical examples and discuss the dependency of the
steady-state mean of the sojourn time of the customers on several
basic system parameters. Utilizing the structural characteristics of
the model we discuss the interpretation of the results. This gives
an insight into the behavior of this tandem queuing model and can be
a base for developing approximations for it.

JIMO

Supervisory control for discrete event systems (DESs) belongs essentially
to the logic level for control problems in DESs. Its corresponding control task is hard. In this
paper, we study a new optimal control problem in DESs. The performance measure is to maximize
the maximal discounted total reward among all possible strings (i.e., paths) of the controlled
system. The
condition we need for this is only that the performance measure is well defined.
We then divide the problem into three sub-cases where the optimal values are respectively
finite, positive infinite and negative infinite. We then show the optimality equation in the
case with a finite optimal value. Also, we characterize the optimality equation together with
its solutions and characterize the structure of the set of all optimal policies. All the results
are still true when the performance measure is to maximize the minimal discounted total reward
among all possible strings of the controlled system.
Finally, we apply these equations and solutions to a resource allocation system. The system may
be deadlocked and in order to avoid the deadlock we can either prohibit occurrence
of some events or resolve the deadlock. It is shown that from the view of the maximal
discounted total cost, it is better to resolve the deadlock if and only if the cost for
resolving the deadlock is less than the threshold value.

JIMO

Peer-to-Peer (P2P) storage systems are a prevalent and important
mode for implementing cost-efficient, large-scale distributed
storage. Considering the random departure feature of the peers and
the diverse popularity of the data objects, a proper number of
replicas needs to be maintained, and a reasonable trigger threshold
of replica repair needs to be set for high data availability and
low system overhead. In this paper, based on the working principle
of the lazy replica repair policy in a P2P storage system, a
three-dimensional Markov chain model is constructed, and the model
is analyzed in steady-state by using a matrix-geometric method.
Then, the performance measures in terms of the availability of one
data object, the average access latency, and the replication rate
are given. Moreover, numerical results with analysis are provided
to demonstrate how system parameters such as the replica number and
the replica repair instant influence the system performance.
Finally, we develop benefit functions to optimize the replica number
and the repair trigger threshold.

DCDS-B

In this paper, we present a new model for optimal control of discrete event systems (DESs) with
an arbitrary control pattern. Here, a discrete event system is defined as a collection of event
sets that depend on strings. When the system generates a string, the next event that may occur
should be in the corresponding event set. In the optimal control model, there are rewards for
choosing control inputs at strings and the sets of available control inputs also depend on
strings. The performance measure is to find a policy under the condition where the discounted
total reward among strings from the initial state is maximized. By applying ideas from Markov
decision processes, we divide the problem into three sub-cases where the optimal value is
respectively finite, positive infinite and negative infinite. For the case with finite optimal
values, the optimality equation is shown and further characterized with its solutions. We also
characterize the structure of the set of all optimal policies. Moreover, we discuss invariance
and closeness of several languages. We present a new supervisory control problem of DESs with
the control pattern being dependent on strings. We study the problem in both the event feedback
control and the state feedback control by generalizing concepts of invariant and closed
languages/predicates. Finally, we apply the above model and results to a job-matching problem.

JIMO

Supervisory control belongs essentially to the logic
level for control problems in discrete event systems (DESs) and its
corresponding control task is hard. This is unlike many practical optimal
control problems which belong to the performance level and whose control
tasks are soft. In this paper, we present two new optimal control problems
of DESs: one with cost functions for choosing control inputs, and the other
for occurring events. Their performance measures are to minimize the maximal
discounted total cost among all possible strings that the system generates.
Since this is a nonlinear optimization problem, we model such systems by
using Markov decision processes. We then present the optimality equations
for both control problems and obtain their optimal solutions. When the cost
functions are stationary, we show that both the optimality equations and
their solutions are also stationary. We then use these equations and
solutions to describe and solve uniformly the basic synthesizing problems in
the two branches of the supervisory control area: those being the event
feedback control and the state feedback control. Moreover, we show that the
control invariant languages and the control invariant predicates with their
permissive supervisors and state feedbacks not only have meanings in
supervisory control of DESs, but are also the optimal solutions for some
optimal control problems. This shows a link existing between the logic level
and the performance level for the control of discrete event systems.
Finally, a numerical example is given to illustrate some results for
supervisory control of a DES.

JIMO

In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.