246,342 research outputs found
Self-stabilizing K-out-of-L exclusion on tree network
In this paper, we address the problem of K-out-of-L exclusion, a
generalization of the mutual exclusion problem, in which there are units
of a shared resource, and any process can request up to units
(). We propose the first deterministic self-stabilizing
distributed K-out-of-L exclusion protocol in message-passing systems for
asynchronous oriented tree networks which assumes bounded local memory for each
process.Comment: 15 page
Strategies for a centralized single product multiclass M/G/1 make-to-stock queue
Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues
Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime. Asymptotics of the stationary distribution
We consider a heterogeneous queueing system consisting of one large pool of
identical servers, where is the scaling parameter. The
arriving customers belong to one of several classes which determines the
service times in the distributional sense. The system is heavily loaded in the
Halfin-Whitt sense, namely the nominal utilization is where
is the spare capacity parameter. Our goal is to obtain bounds on the
steady state performance metrics such as the number of customers waiting in the
queue . While there is a rich literature on deriving process level
(transient) scaling limits for such systems, the results for steady state are
primarily limited to the single class case.
This paper is the first one to address the case of heterogeneity in the
steady state regime. Moreover, our results hold for any service policy which
does not admit server idling when there are customers waiting in the queue. We
assume that the interarrival and service times have exponential distribution,
and that customers of each class may abandon while waiting in the queue at a
certain rate (which may be zero). We obtain upper bounds of the form
on both and the number of idle servers. The bounds
are uniform w.r.t. parameter and the service policy. In particular, we show
that . Therefore, the
sequence is tight and has a uniform exponential tail
bound. We further consider the system with strictly positive abandonment rates,
and show that in this case every weak limit of
has a sub-Gaussian tail. Namely .Comment: 21 page
Spare parts provisioning for multiple k-out-of-n:G systems
In this paper, we consider a repair shop that fixes failed components from different k-out-of-n:G systems. We assume that each system consists of the same type of component; to increase availability, a certain number of components are stocked as spare parts. We permit a shared inventory serving all systems and/or reserved inventories for each system; we call this a hybrid model. Additionally, we consider two alternative dispatching rules for the repaired component. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our analysis gives the steady-state system size distribution of the two alternative
models at the repair shop. We conduct numerical examples minimizing the spare parts held while subjecting the availability of each system to exceed a targeted value. Our findings show that unless the availabilities of systems are close, the HP policy is better than the HF policy
The Origin of [OII] in Post-Starburst and Red-Sequence Galaxies in High-Redshift Clusters
We present the first results from a near-IR spectroscopic campaign of the
Cl1604 supercluster at z~0.9 and the cluster RX J1821.6+6827 at z~0.82 to
investigate the nature of [OII] 3727A emission in cluster galaxies at high
redshift. Of the 401 members in the two systems, 131 galaxies have detectable
[OII] emission with no other signs of current star-formation, as well as strong
absorption features indicative of a well-established older stellar population.
The combination of these features suggests that the primary source of [OII]
emission in these galaxies is not the result of star-formation, but rather due
to the presence of a LINER or Seyfert component. Using the NIRSPEC spectrograph
on the Keck II 10-m telescope, 19 such galaxies were targeted, as well as six
additional [OII]-emitting cluster members that exhibited other signs of ongoing
star-formation. Nearly half (~47%) of the 19 [OII]-emitting, absorption-line
dominated galaxies exhibit [OII] to Ha equivalent width ratios higher than
unity, the typical value for star-forming galaxies. A majority (~68%) of these
19 galaxies are classified as LINER/Seyfert based on the emission-line ratio of
[NII] and Ha, increasing to ~85% for red [OII]-emitting, absorption-line
dominated galaxies. The LINER/Seyfert galaxies exhibit L([OII])/L(Ha) ratios
significantly higher than that observed in populations of star-forming
galaxies, suggesting that [OII] is a poor indicator of star-formation in a
large fraction of high-redshift cluster members. We estimate that at least ~20%
of galaxies in high-redshift clusters contain a LINER/Seyfert component that
can be revealed with line ratios. We also investigate the effect this
population has on the star formation rate of cluster galaxies and the
post-starburst fraction, concluding that LINER/Seyferts must be accounted for
if these quantities are to be meaningful.Comment: 33 pages, 17 figures, to appear in Ap
On deciding stability of multiclass queueing networks under buffer priority scheduling policies
One of the basic properties of a queueing network is stability. Roughly
speaking, it is the property that the total number of jobs in the network
remains bounded as a function of time. One of the key questions related to the
stability issue is how to determine the exact conditions under which a given
queueing network operating under a given scheduling policy remains stable.
While there was much initial progress in addressing this question, most of the
results obtained were partial at best and so the complete characterization of
stable queueing networks is still lacking. In this paper, we resolve this open
problem, albeit in a somewhat unexpected way. We show that characterizing
stable queueing networks is an algorithmically undecidable problem for the case
of nonpreemptive static buffer priority scheduling policies and deterministic
interarrival and service times. Thus, no constructive characterization of
stable queueing networks operating under this class of policies is possible.
The result is established for queueing networks with finite and infinite buffer
sizes and possibly zero service times, although we conjecture that it also
holds in the case of models with only infinite buffers and nonzero service
times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002)
272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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