**3 ^{rd} Korea-Netherlands workshop on **

**
"Queueing theory and its applications to telecommunication systems" (QPA)**

**July 12, 2007**

**EURANDOM, Eindhoven, The Netherlands**

**ABSTRACTS**

**Sem Borst (Alcatel-Lucent Bell Labs & Eindhoven
University of Technology)
**Joint work with Maaike Verloop (CWI) and Rudesindo
Nunez-Queija (CWI & TNO ICT)

**Delay Optimization in Bandwidth-Sharing Networks **

Bandwidth-sharing networks as considered by Massoulie & Roberts provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Although valuable stability results have been obtained, crucial performance metrics such as flow-level delays and throughputs in these models have remained intractable in all but a few special cases. In particular, it is not well understood to what extent flow-level delays and throughputs achieved by standard bandwidth-sharing mechanisms such as alpha-fair strategies leave potential room for improvement.

In order to gain a better understanding of the latter issue, we determine the scheduling policies that minimize the mean delay in some simple linear bandwidth-sharing networks. We compare the performance of the optimal policy with that of various alpha-fair strategies so as to assess the efficacy of the latter and gauge the potential room for improvement. The results indicate that the optimal policy achieves only modest improvements, even when the value of alpha is simply fixed, provided it is not too small.

**Bong Dae Choi (Korea University)
**Joint work with Eunju Hwang, Kyung Jae Kim , Jung Je Son,
Korea University

**Power saving mechanisms in the IEEE
802.16e : Periodic traffic indications and binary traffic indications
**

We propose a new sleep-mode scheme called the *power saving
mechanism with periodic traffic indications* in the IEEE 802.16e. In the
proposed scheme, traffic indication (TRF-IND) messages are regularly sent at
every constant time to initiate transmission. Bandwidth and energy can be saved
by not sending sleep request (MOB-SLP-REQ) and sleep response (MOB-SLP-RSP)
messages, which are required in the original power saving classes in the 802.16e
standard. We derive the Laplace Stieltjes transforms (LSTs) of the lengths of
awake interval and sleep interval as well as the LST of queueing delay of a
message. As performance measures we obtain sleep-mode ratio, power-consumption
ratio, and mean total-delay. We show that our analytic results match with
simulation results very well. Using our performance analysis we find the optimal
system parameters such as a TRF-IND interval and a close-down time, which
minimize the power consumption of MS while satisfying the required quality of
service (QoS) on mean total-delay. The numerical results show that the proposed
scheme performs better than the original power saving class of type 1 in the
standard.

**Gang Uk Hwang (Korea Advanced Institute
of Science and Technology)
**Joint works with Fumiio Ishizaki,
Korea Advanced Institute of Science and Technology

**Cross-layer design with adaptive
modulation and coding scheme for QoS support and its theoretical
analysis **

In this paper, we consider a cross-layer design problem of a wireless network with AMC (Adaptive Modulation and Coding). In our cross-layer design, the average packet transmission error rate at the PHY layer and the packet overflow probability at the MAC layer are simultaneously investigated. In addition, we assume that packet retransmission is allowed for the packets received in error and that a certain level of packet overflow probability at the MAC layer is given as the QoS (Quality of Service) requirement. To capture the joint effect of the performances of both layers, we introduce the effective bandwidth function of the packet service process at the MAC layer. For our cross-layer design, we provide a theoretical analysis on the behavior of the effective bandwidth function when we change the AMC scheme at the PHY layer. Based on our theoretical results, we propose a new framework for our cross-layer design, with which we can meet the required packet overflow probability at the MAC layer while maintaining the average packet transmission error rate at the PHY layer as low as possible. A numerical example is provided to see the validity of the proposed framework and to investigate its characteristics.

**Bara Kim (Korea University)
**Joint work with Jerim Kim, Korea University

**Regularly varying tail of the waiting
time distribution in the M/G/1 retrial queue**

We consider an M/G/1 retrial queue, where the service time
distribution has a regularly varying tail with

index -*b**,* < 1 *b*
< 2. The waiting time distribution is shown to have a regularly varying
tail with index 1 -* b, *and the pre-factor is
determined explicitly. The result is obtained by comparing the waiting time in
the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with
random order service policy.

**Rein Nobel (Vrije Universiteit Amsterdam)**

**A retrial queueing system with a variable number of active servers **

A retrial queueing model is considered with Poisson input and an infinite number of servers. At any epoch only a finite number of the servers are active, the others are called dormant. An active server is always in one of two possible states, idle or busy. Linear operating costs are incurred for the active servers. These costs will be higher for busy servers than for idle servers. When upon arrival of a customer at least one of the active servers is idle, the newly arrived customer goes into service immediately, making the idle server busy. When at an arrival epoch all active servers are busy, the decision must be made to send the newly arrived customer into orbit, or to activate a dormant server for immediate service of the arrived customer. Activating a dormant server requires a set-up cost. Customers in orbit try to reenter the system after an exponentially distributed retrial time. All retrial times are independent and identically distributed. For each customer in orbit linear holding costs are incurred. At service completion epochs the decision must be made to keep the newly become idle server active, or to make this server dormant. The service times of the customers are independent and have the same Coxian-2 distribution. The problem is when to activate and shut down servers in order to minimize the cost per unit time.

An efficient algorithm is discussed for calculating an optimal policy for activating dormant servers at arrival epochs and shutting down active servers at service completion epochs.

**Jan Kees van Ommeren (University of Twente)**

**Network Performance under Mobility in Ad Hoc Networks **

In this talk we consider wireless networks with moving nodes. Due to the mobility, nodes can not always communicate. For small networks, with one intermediate moving node, we present a polling model with a so-called autonomous server.

In existing polling models, the focus often is on controlling the operation of the server as to optimize some performance measure. For our system, controlling the server is not an issue as the server moves independently in the system.

We present the analysis for such a polling model with an autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for.

**JinSoo Park (Advanced Research Laboratory, KT)
**Joint work with HakJin Chong, Advanced Research Laboratory,
KT

**Overviews on wireless mesh networking
technologies **

Wireless mesh networking (WMN) technologies have captured attention from both industry and academia recently, and they can be the ultimate wireless networking solution for the next decade. WMNs are characterized as having self-configuring and self-healing nature along with flexible interoperability with other networks. In this paper, we discuss a few promising wireless mesh networking technologies, especially those from IEEE 802.15.5, IEEE 802.11s, 6LoWPAN standards, and address a few crucial research issues that are associated with the standards.

**Balakrishna Prabhu (CWI, TU/e, EURANDOM)
**Joint work with Rudesindo Nunez-Queija (CWI & TNO ICT

**Scaling laws for file dissemination in P2P networks with random contacts**

In this talk, we present the scaling law for broacast time of a file in a P2P network with an initial population of $N$ nodes. In the model we consider, at Poisson rate $\lambda$ a node intiates a contact with another node chosen uniformly at random. This contact is said to be successful if the contacted node possess the file in which case the initiator is able to download the file. In a network with altruistic nodes (i.e., nodes do not leave the network) we show that the broadcast time is $O(\log(N))$. In a network with selfish nodes, our main result shows that $O(\log(N))$ broadcast time can be achieved if nodes remain connected to the network for the duration of at least one more contact after downloading the file, otherwise a significantly worse $O(N)$ time is required to broadcast the file.

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