Detecting Markov Chain Instability: A Monte Carlo Approach

We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. The theoretical underpinnings of our algorithm are based on a result stating that the stability of a set of parameters can be phrased in terms of the stability of a single Markov chain that searches the set for unstable parameters. Our framework leads to a procedure that is capable of performing statistically rigorous tests for instability, which has been extensively tested using several examples of standard and non-standard queueing networks

The snowball effect of customer slowdown in critical many-server systems

Customer slowdown describes the phenomenon that a customer's service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient's delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.Comment: 23 pages, 8 figures -- version 3 fixes a typo in an equation. in Stochastic Models, 201

Analysis of State-Independent Importance-Sampling Measures for the Two-Node Tandem Queue

We investigate the simulation of overflow of the total population of a Markovian two-node tandem queue model during a busy cycle, using importance sampling with a state-independent change of measure. We show that the only such change of measure that may possibly result in asymptotically efficient simulation for large overflow levels is exchanging the arrival rate with the smallest service rate. For this change of measure, we classify the model's parameter space into regions of asymptotic efficiency, exponential growth of the relative error, and infinite variance, using both analytical and numerical techniques

Efficient T-CONT-agnostic Bandwidth and Wavelength Allocation for NG-PON2

Dynamic bandwidth and wavelength allocation are used to demonstrate high quality of service (QoS) in time wavelength-division multiplexed–passive optical networks (TWDM-PONs). Both bandwidth and wavelength assignment are performed on the basis of transmission containers (T-CONTs) and therefore by means of upstream service priority traffic flows. Our medium access control (MAC) protocol therefore ensures consistency in processing alike classes of service across all optical network units (ONUs) in agreement with their QoS figures. For evaluation of the MAC protocol performance, a simulator has been implemented in OPNET featuring a 40 km, 40 Gbps TWDM-PON with four stacked wavelengths at 10 Gbps each and 256 ONUs. Simulation results have confirmed the efficiency of allocating bandwidth to each wavelength and the significant increase of network traffic flow due to adaptive polling from 9.04 to 9.74 Gbps. The benefit of T-CONT-centric allocation has also been measured with respect to packet delay and queue occupancy, achieving low packet delay across all T-CONTs. Therefore, improved NG-PON2 performance and greater efficiency are obtained in this first demonstration of T-CONTs allocated to both wavelength and time.Peer reviewe

The network queueing system

Described is the implementation of a networked, UNIX based queueing system developed on contract for NASA. The system discussed supports both batch and device requests, and provides the facilities of remote queueing, request routing, remote status, queue access controls, batch request resource quota limits, and remote output return

Collective Bargaining under Non-Binding Contracts

We introduce collective bargaining in a static framework where the firm and its risk-neutral employees negotiate over wages in a non-binding contract setting. Our main result is the equivalence between the non-binding collective equilibrium wage-employment contract and the equilibrium contract under binding risk-neutral efficient bargaining. We also demonstrate that our non-cooperative equilibrium wages and profits coincide with the Owen values of the corresponding cooperative game with the coalitional structure that follows from unionization.collective bargaining, union, firm, bargaining power, non-binding contract