The so-called “Israeli queue” (Boxma et al. in Stoch Model 24(4):604– 625, 2008; Perel and Yechiali in Probab Eng Inf Sci, 2013; Perel and Yechiali in Stoch Model 29(3):353–379, 2013) is a multi-queue polling-type system with a single server. Service is given in batches, where the batch sizes are unlimited and the service time of a batch does not depend on its size. After completing service, th...

In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a parameter k defined as the system size of the finite approximation. The approximations capture the interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of the departures from an ME/ME/1 queue up to lag (k − 1).

We study the impact of service time distributions on the distribution ofthe maximum queue length during a busy period for the Mx/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come-first-served discipline,...

Router queues can impact both round-trip times and throughput. Yet little is publicly known about queue provisioning employed by Internet services providers for the routers that control the access links to home computers. This paper proposes QFind, a black-box measurement technique, as a simple method to approximate the size of the access queue at last mile router. We evaluate QFind through sim...

Random Early Detection (RED) has been introduced as a congestion avoidance algorithm for the Internet. RED detects congestion by estimating the average queue size. It drops packets probabilistically before buuer overrow, with the drop probability depending on the average queue size. In this paper, we analyse the innuence of RED on the packet loss ratio and the throughput of a system consisting ...

In this paper we analyze the performance of 802.15.4 Wireless Sensor Network (WSN) and derive the queue size trade off for different modulation schemes like: Minimum Shift Keying (MSK), Quadrature Amplitude Modulation of 64 bits (QAM_64) and Binary Phase Shift Keying (BPSK) at the radio transmitter of different types of devices in IEEE 802.15.4 for WSN. It is concluded that if queue size at the...

This paper studies the Ethernet Passive Optical Network (EPON) with gated-limited service. The transmission window (TW) is limited in this system to guaranteeing a bounded delay experienced by disciplined users, and to constrain malicious users from monopolizing the transmission channel. Thus, selecting an appropriate TW size is critical to the performance of EPON with gated-limited service dis...

Consider a single channel two station tandem queue with zero queue capacity and with blocking (Taha, 1989). Assuming that the arrival process and the service process are dependent, we obtain the transient solution for the system when the joint distribution of interarrival time, service time at Station1 and service time at Station 2 is trivariate exponential. Also, CAN estimators and asymptotic ...

We consider the problem of implementing shared objects in uniprocessor and multiprocessor real-time systems in which tasks are executed using a scheduling quantum. In most quantum-based systems, the size of the quantum is quite large in comparison to the length of an object call. As a result, most object calls can be expected to execute without preemption. A good object-sharing scheme should op...

We develop approximate solutions for the equilibrium queue length probability distribution of queues in open Markovian networks by considering each queue independently, constructing its arrival process as the join of each contributing queue's departing traffic. Without modulation and non-unit batches, we would only need to consider mean internal traffic rates, modelling each queue as M/M/1 to g...