Benny Van Houdt

An integrated production and inventory model to dampen upstream demand variability in the supply chain

Abstract We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.

Performance of garbage collection algorithms for flash-based solid state drives with hot/cold data

To avoid a poor random write performance, flash-based solid state drives typically rely on an internal log-structure. This log-structure reduces the write amplification and thereby improves the write throughput and extends the drives lifespan. In this paper, we analyze the performance of the log-structure combined with the d-choices garbage collection algorithm, which repeatedly selects the block with the fewest number of valid pages out of a set of d randomly chosen blocks, and consider non-uniform random write workloads. Using a mean field model, we show that the write amplification worsens as the hot data gets hotter. Next, we introduce the double log-structure, which uses a separate log for internal and external write requests. Although the double log-structure performs identically to the single log-structure under uniform random writes, we show that it drastically reduces the write amplification of the d-choices algorithm in the presence of hot data. In other words, the double log-structure yields an automatic form of data separation. Further, with the double log-structure there exists an optimal value for d (typically around 10), meaning the greedy garbage collection algorithm is no longer optimal. Finally, both mean field models introduced in this paper are validated using simulation experiments.

A win–win solution for the bullwhip problem

An important supply chain research problem is the bullwhip effect where demand variability increases as one moves up the supply chain. This distorted information may lead to inefficiencies. In this article we suggest a remedy to reduce the bullwhip effect. We focus on an inventory replenishment rule that reduces the variability of upstream orders and generates a smooth order pattern. However, dampening the order variability has a negative impact on customer service due to an increased inventory variance. We resolve this conflicting issue by taking the impact of the replenishment rule on lead times into account. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the inventory levels. We show that by including endogenous lead times in our analysis, the order pattern can be smoothed to a considerable extent without increasing stock levels, resulting in a win–win solution for both supply chain echelons. Finally we discuss several order smoothing approaches from an industrial perspective and comment on how our results may influence these cases.

Transient and Steady-state Regime of a Family of List-based Cache Replacement Algorithms

In this paper we study the performance of a family of cache replacement algorithms. The cache is decomposed into lists. Items enter the cache via the first list. An item enters the cache via the first list and jumps to the next list whenever a hit on it occurs. The classical policies FIFO, RANDOM, CLIMB and its hybrids are obtained as special cases. We present explicit expressions for the cache content distribution and miss probability under the IRM model. We develop an algorithm with a time complexity that is polynomial in the cache size and linear in the number of items to compute the exact miss probability. We introduce lower and upper bounds on the latter that can be computed in a time that is linear in the cache size times the number of items. We further introduce a mean field model to approximate the transient behavior of the miss probability and prove that this model becomes exact as the cache size and number of items tends to infinity. We show that the set of ODEs associated to the mean field model has a unique fixed point that can be used to approximate the miss probability in case the exact computation becomes too time consuming. Using this approximation, we provide guidelines on how to select a replacement algorithm within the family considered such that a good trade-off is achieved between the cache reactivity and its steady-state hit probability. We simulate these cache replacement algorithms on traces of real data and show that they can outperform LRU. Finally, we also disprove the well-known conjecture that the CLIMB algorithm is the optimal finite-memory replacement algorithm under the IRM model.

Dynamic bandwidth allocation algorithms in EPON: a simulation study

In this paper we present a dynamic bandwidth allocation algorithm for EPON, which makes use of the Multipoint Control Protocol (MPCP) with threshold reporting and with inter- and intra-ONU priority scheduling. Three varieties of this algorithm are compared, by means of a detailed simulation program, regarding average packet delay for several priorities, delay variation for constant bit rate (CBR) traffic and bandwidth utilization. We show that by introducing a specific intra-ONU priority scheduling algorithm, which takes the reported values into account, the bandwidth can be fully utilized. However, this scheduling algorithm causes an increased packet delay and delay variation for CBR traffic. In order to eliminate this drawback, we combine this scheduling algorithm with a rate-based scheme for the highest priority (CBR) traffic. This combined algorithm provides an interesting tradeoff between the efficiency, which is still near to the optimal, and the delay characteristics of time critical applications. Finally, we also include a comparison with a standard intra-ONU priority scheme.

Optimization of a packet video receiver under different levels of delay jitter: an analytical approach

This paper studies the problem of analyzing and designing optimal playout adaptation policies for packet video receivers (PVRs) that operate in a delay jitter inducing best-effort network, like the current Internet. The developed system model is built around the Ek/Di/1/N phase-type queue and allows for the effective modeling of key design and system parameters, such as: the level of delay jitter, the performance metrics and the employed playout policy. The optimal playout policy is derived under k-Erlang interarrivals by formulating and solving an optimization problem. The (theoretical) optimal solution is transformed into an approximately optimal one that utilizes observable information and it is, thus, feasible. Numerical results are derived under the optimal policy and compared against those under the optimal policy that assumes a fixed level of jitter as determined by Poisson arrivals, as well as against the deterministic service that applies no playout adaptation. Based on this work, a PVR is proposed that adapts to varying network delay jitter and tries to induce a performance that approximates the derived theoretical optimal one.

Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience

In this paper we introduce the adaptive MMAP[K] arrival process and analyze the adaptive MMAP[K]/PH[K]/1 queue. In such a queueing system, customers of K different types with Markovian inter-arrival times and possibly correlated customer types, are fed to a single server queue that makes use of r thresholds. Service times are phase-type and depend on the type of customer in service. Type k customers are accepted with some probability ai,k if the current workload is between threshold i−1 and i. The manner in which the arrival process changes its state after generating a type k customer also depends on whether the customer is accepted or rejected.

Triangular M/G/1-Type and Tree-Like Quasi-Birth-Death Markov Chains

In applying matrix-analytic methods to M/G/1-type and tree-like quasi-birth-death (QBD) Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1-type and tree-like QBD Markov chains that allows for an efficient direct solution of the matrix equation.

Wavelength allocation in an optical switch with a fiber delay line buffer and limited-range wavelength conversion

This paper presents an approach to evaluate the performance of an optical switch equipped with both limited-range wavelength conversion and Fiber Delay Lines to resolve contention. We propose an analytical model that allows a general behavior for the packet size distribution while the inter-arrival times are assumed to be of Phase-Type and can easily be relaxed to be generally distributed if needed. As the set of reachable wavelengths is a major issue in limited-range wavelength conversion, we first focus on a simple wavelength set configuration that allows the comparison of different policies and their effect on the loss rate of the system. In addition, a linear association between the loss rate of the simple and a more complex set configuration is identified. Using this association and the results from the analytical model, we derive an approximation for the more complex case, where the interactions among adjacent wavelengths play an important role. The approximation works well for different parameter instances and is particularly useful for the mid load case, when simulations become computationally prohibitive.

The impact of buffer finiteness on the loss rate in a priority queueing system

This paper discusses five different ways to approximate the loss rate in a fundamental two class priority system, where each class has its own finite capacity buffer, as well as an exact approach. We identify the type of error one can expect by assuming that one, or both buffers are of infinite size. Furthermore, we investigate whether asymptotic based results can achieve the same level of accuracy as those based on the actual steady state probabilities. Three novel priority queueing models are introduced and efficient algorithms, relying on matrix analytic methods, are developed within this context. A comparative study based on numerical examples is also included