NP call setup time evaluation

When caches are applied to PBX, every outgoing call brings about a cache query for routing address translation. The result of cache queries could be cache hit (i.e., the cached data represent the correct routing address of the dialed number) or cache miss.

In the case of cache hit, the routing address would be translated in PBX and the call would be routed to the called party directly without querying NPAC. In the case of cache miss, NPAC query is necessary to obtain the routing address of the called party.

Location miss (i.e., the cached data is obsolete) will not occur because of the policy of postponed activity of new ported numbers.

PBX Switch Switch PBX

Cache ^{Network 1} NPAC ^{Network 2} Cache

t_local-1 t_long t_local-2

Fig. 3-4 Simplified NP call setup stages and time table

The NP call setup stages can be simplified and represented as Fig. 3-4. Where tlocal-1 and tlocal-2 are the local transmission delay in the service region of an operator network, tlong is the delay time of cross-operator networks transmission. Let tcache and tNPAC be the routing address translation latency of cache access and NPAC query, respectively. According to Fig. 3-4, the NP call setup time of location-hit of PBX-cache (tcache-hit), cache- miss of PBX-cache (tcache-miss), and conventional scenario (tconv) can be represented as in the following.

l NP call setup time of conventional telecommunication environment:

tconv =( tlocal-1 + tlocal-2) + tlong + tNPAC

= tlocal + tlong + tNPAC (4)

l NP call setup time of PBX-cache environment in the case of location hit:

tcache-hit = tlocal + tlong + tcache

= tconv – (tNPAC - tcache)

l NP call setup time of PBX-cache environment in the case of cache miss:

tcache-miss = tlocal + tlong + tcache + tNPAC

= tlocation-hit + tNPAC

= tconv + tcache

Let the cache hit rate in a PBX be p, 0= p = 1, which equals to the probability of that a number in the FDN set being dialed. The call setup time in PBX-cache environme nt can be depicted as

tPBX-cache = p × tcache-hit + (1- p) × tcache-miss

= p × [tconv – (tNPAC - tcache)] + (1- p) × (tconv + tcache)

= p × tconv – p × (tNPAC – tcache) + (1- p) ×(tconv + tcache)

= tconv + tcache + p × tNPAC (5)

From (5), the call setup time of PBX-cache is proportional to (1- p). The more frequent FDN are dialed, the less the call setup delay is. Comparing the NP call setup time of conventional and PBX-cache applied environment:

)

From (6), we can say that PBX-cache benefits when p, the probability of dialing a FDN, increases. The figure as shown in Fig. 3-5 depicts the relation of NP call setup time decreases as p increases.

NP call setup delay

Fig. 3-5 The relation of FDN utility rate (p) and the average call setup time (in msec) The message transmission time of every trunk can be represented as

(message length / transmission rate of the trunk) + (trunk length/velocity of light or velocity of electrons).

With respect to Fig. 3-4, the message transmission delay within an operator network (tlocal) and between operator networks (tlong) can be calculated. The time for querying routing information from NPAC (tNPAC) should be less than 2 seconds [5], and the memory access time for searching data form a cache (tcache) is assumed as 0.001 msec.

Assuming the transmission media beyond PBX is optical fiber, and within a PBX service region is twisted pair. The scope of connections within a PBX is 1km, connections between PBX and the local exchange spread from 1km to 10 km. The scope of long-term connections among different telecom service networks follows the geographical length of Taiwan (it is 390km), assuming the longest connection is less than 450 km. The size of calling signals is assumed to be 180 bits (ISUP IAM and added special codes). Suppose the time to process an ISUP IAM message is 100msec, which includes the time for signal codec, routing process, and network resource allocation. For service providers, each database handles 8 million calls per day; that is, 435 calls per second [23]. NPDB query must complete within 2 seconds or less [15].

A PBX handles 2000 calls per hour, and 8 calls per second in the rush hours. The delay of searching a cached entry is less than 1/100 millisecond in average.

Considering there are 10 thousands members in a PBX service region, every user has a set of 30 FDN in average. The setup time of a call is 4000 milliseconds without implementing caches to PBX. Fig. 3-5 demonstrates the relation of FDN utility rate p and the average call setup time with a cache in PBX. When 30% of the calls are made to frequent contact objects (i.e., 30% of cache queries are hit. While location miss will not happen, all the calls are location hit), the setup time of a call reduced to 3550 msec in average, 11.25% of the call setup time is saved. The NP call setup time decreases when the dialed numbers has locality and the probability of dialing a number in the FDN set increases. When 70% of the dialed numbers are FDN, and the call setup time decreased to 2950 msec. 30% of call setup time is reduced.

Assume the average calling rate is 450 calls per hour of an organization with 10-thousand employees. 70% of the outgoing calls are set to numbers in the FDN set.

iNetwork with can shorten 0.7 × (4000-2950) = 735 milliseconds call setup delay for every call in average. Thus, the shortened call setup time is (0.735 second × 450 calls)

= 330.75 seconds/per hour. For 8 hours office time per day, the cache can save the organization (330.75 × 8)/60 = 44.1 minutes = 0.735 man- hour per day. For 22 working days per month, (0.735 × 22 × 12) = 194.04 man-hour per year are saved for an organization.

In the peak-time the NPDB workload capacity will not detain the call setup process. As the traffic originated from enterprises increase in the peak time, the increase of FDN utilization prominently alleviates the requirement of NPDB accesses.

Assume there are 10-thousand calls per hour arrive a switching center in office hours,

and 70% of the calls are dialed from organizations. Let 85% of the 7000 calls are issued from PBX with cache, and the probability of cache hit is p. Consequently, there are (7000 × 85% × p) NP calls are translated without querying NPDB searches. Let 70% of number dialed from organizations are FDN (the cache hit rate is p = 0.7), 4164 calls need not search NPDB; when 90% of calls dialed from organizations are FDN, 5355 NPDB queries are omitted. That is, 41.64% and 53.55% of NPDB workload is alleviated in the case of p = 0.7 and p = 0.9, respectively.

SCP access times (p=0.7)

0 100 200 300 400 500

50 100 150 200 250 300 350 400 450 a

SCP access_cache SCP access_no cache

Fig. 3-6 The SCP access frequency

SCP access times

0 100 200 300 400 500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p

SCP access_cache SCP access_no cache

Fig. 3-7 The frequency of SCP accesses when the arrival rate is 450 (calls/hr)

From another point of view, users will hand up a call and re-dial the same number again when the call setup time is too long to be tolerable. The re-dials bring about more signals and consume more network resources. Operators need to take the overhead without any revenue. The shortened NP call setup delay results in the decrease of re-dials, and the network resource can be utilized more effectively.

From the above, applying caches to PBX to enable ported number translation in PBX can remarkably avoid a great part of NPAC queries. Which alleviate the workload of the public switching network and shorten the average NP call setup time.

The improved NP call setup efficiency results in better communication resource utilization; therefore, caches on PBX benefit both the telecommunication service providers and users.