scholarly journals Calculation of delay characteristics for multiserver queues with constant service times

2009 ◽  
Vol 199 (1) ◽  
pp. 170-175 ◽  
Author(s):  
Peixia Gao ◽  
Sabine Wittevrongel ◽  
Joris Walraevens ◽  
Marc Moeneclaey ◽  
Herwig Bruneel
Keyword(s):  
Multiserver Queues ◽  
Service Times ◽  
Constant Service Times

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (02) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates. These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (2) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates.These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

scholarly journals The queue-length in GI/G/s queues

2000 ◽  
Vol 6 (1) ◽  
pp. 1-11
Author(s):  
Pierre Le Gall
Keyword(s):  
Queue Length ◽  
Buffer Capacity ◽  
Service Times ◽  
Constant Service Times

The distribution of the queue-length in the stationary symmetrical GI/G/s queue is given with an application to the M/G/s queue, particularly in the case of the combination of several packet traffics, with various constant service times, to dimension the buffer capacity.

Overflow processes for multiserver queues with finite waiting room

1984 ◽  
Vol 16 (1) ◽  
pp. 8-8
Author(s):  
Jos H. A. De Smit
Keyword(s):  
Renewal Process ◽  
Numerical Results ◽  
Markov Renewal Process ◽  
Waiting Room ◽  
Multiserver Queues ◽  
Phase Type ◽  
Service Times ◽  
Overflow Process ◽  
Explicit Expressions

The overflow process of the multiserver queue with phase-type service times and finite waiting room is a Markov renewal process. The solution for this process is obtained. If the service times are exponential the overflow process reduces to a renewal process. For the latter case explicit expressions and numerical results are given.

scholarly journals The asymptotic variance of departures in critically loaded queues

2011 ◽  
Vol 43 (01) ◽  
pp. 243-263 ◽  
Author(s):  
A. Al Hanbali ◽  
M. Mandjes ◽  
Y. Nazarathy ◽  
W. Whitt
Keyword(s):  
Explicit Expression ◽  
Counting Process ◽  
Asymptotic Variance ◽  
Arrival Rate ◽  
Finite Capacity ◽  
System Load ◽  
Multiserver Queues ◽  
Service Patterns ◽  
Coefficients Of Variation ◽  
Service Times

We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies lim t→∞varD(t) / t = λ(1–2/π)(c a 2 + c s 2), where λ is the arrival rate, and c a 2 and c s 2 are squared coefficients of variation of the interarrival and service times, respectively. As a consequence, the departures variability has a remarkable singularity in the case in which ϱ equals 1, in line with the BRAVO (balancing reduces asymptotic variance of outputs) effect which was previously encountered in finite-capacity birth-death queues. Under certain technical conditions, our result generalizes to multiserver queues, as well as to queues with more general arrival and service patterns. For the M/M/1 queue, we present an explicit expression of the variance of D(t) for any t.

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